%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "5.34",
%%% date = "16 May 2012",
%%% time = "11:37:02 MDT",
%%% filename = "elefunt.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "59216 44519 184847 1904196",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "BibTeX; bibliography; convergence
%%% acceleration; elementary functions; sequence
%%% acceleration; special functions",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a bibliography of publications about
%%% the computation of the elementary functions
%%% (square root, exponential, logarithm,
%%% trigonometric, inverse trigonometric,
%%% hyperbolic, inverse hyperbolic, ...), and
%%% some selected special functions (Bessel,
%%% elliptic integral, exponential integral,
%%% Gamma, log-Gamma, psi, ...), in computer
%%% programming languages. Additional references
%%% to articles, books, and conference
%%% proceedings provide more mathematical
%%% background.
%%%
%%% At version 4.00, this bibliography was
%%% significantly extended by merging in the 262
%%% entries from the bibliography given in entry
%%% Fullerton:1980:BEM. That document was not
%%% available electronically on the Internet, and
%%% the original bib/refer bibliography data from
%%% which the report was derived may have been
%%% lost with the death of its author, so a
%%% printed copy of the report was scanned and
%%% converted to searchable text. Its entries
%%% were then compared with the previous contents
%%% of this file, and the extensive collections
%%% in the TeX User Group and BibNet Project
%%% archives. All of the publications that
%%% Fullerton covered are marked with a citedby
%%% keyword, and his notes are included in remark
%%% keyword values prefixed by his name.
%%%
%%% At version 5.00 of 1-Dec-2011, numerous
%%% references on hypergeometric functions and on
%%% convergence acceleration of sequences were
%%% added. Particularly with special functions,
%%% many standard series expansions converge too
%%% slowly to be useful, but acceleration
%%% techniques can sometimes provide a dramatic
%%% improvement, making such sums numerically
%%% practical. The new entries in that area all
%%% contain the phrase `convergence acceleration'
%%% in their keywords values. See entry
%%% Willis:2012:AGH for a good recent survey of
%%% both areas.
%%%
%%% At version 5.34, the year coverage looked
%%% like this:
%%%
%%% 1925 ( 1) 1955 ( 4) 1985 ( 34)
%%% 1926 ( 1) 1956 ( 1) 1986 ( 30)
%%% 1927 ( 0) 1957 ( 8) 1987 ( 34)
%%% 1928 ( 0) 1958 ( 6) 1988 ( 48)
%%% 1929 ( 0) 1959 ( 12) 1989 ( 85)
%%% 1930 ( 0) 1960 ( 14) 1990 ( 32)
%%% 1931 ( 0) 1961 ( 19) 1991 ( 47)
%%% 1932 ( 0) 1962 ( 14) 1992 ( 35)
%%% 1933 ( 0) 1963 ( 29) 1993 ( 41)
%%% 1934 ( 1) 1964 ( 42) 1994 ( 47)
%%% 1935 ( 0) 1965 ( 33) 1995 ( 40)
%%% 1936 ( 0) 1966 ( 21) 1996 ( 27)
%%% 1937 ( 2) 1967 ( 25) 1997 ( 33)
%%% 1938 ( 0) 1968 ( 30) 1998 ( 26)
%%% 1939 ( 0) 1969 ( 34) 1999 ( 48)
%%% 1940 ( 1) 1970 ( 33) 2000 ( 31)
%%% 1941 ( 1) 1971 ( 29) 2001 ( 30)
%%% 1942 ( 1) 1972 ( 32) 2002 ( 21)
%%% 1943 ( 1) 1973 ( 28) 2003 ( 25)
%%% 1944 ( 3) 1974 ( 24) 2004 ( 33)
%%% 1945 ( 2) 1975 ( 26) 2005 ( 23)
%%% 1946 ( 1) 1976 ( 32) 2006 ( 21)
%%% 1947 ( 0) 1977 ( 35) 2007 ( 25)
%%% 1948 ( 2) 1978 ( 31) 2008 ( 19)
%%% 1949 ( 2) 1979 ( 31) 2009 ( 27)
%%% 1950 ( 1) 1980 ( 27) 2010 ( 16)
%%% 1951 ( 3) 1981 ( 40) 2011 ( 30)
%%% 1952 ( 3) 1982 ( 42) 2012 ( 7)
%%% 1953 ( 1) 1983 ( 36) 2013 ( 1)
%%% 1954 ( 4) 1984 ( 47)
%%%
%%% Article: 1236
%%% Book: 113
%%% InBook: 1
%%% InCollection: 47
%%% InProceedings: 161
%%% Manual: 1
%%% MastersThesis: 4
%%% Misc: 12
%%% Periodical: 1
%%% PhdThesis: 16
%%% Proceedings: 76
%%% TechReport: 61
%%% Unpublished: 3
%%%
%%% Total entries: 1732
%%%
%%% This bibliography has been collected from
%%% bibliographies in the author's personal
%%% files, from the OCLC WorldCat and
%%% Contents1st databases, from the American
%%% Mathematical Society MathSciNet database,
%%% from the ACM Computing Archive CD-ROM,
%%% and from the computer science bibliography
%%% collection on ftp.ira.uka.de in
%%% /pub/bibliography to which many people of
%%% have contributed.
%%%
%%% Numerous errors in the sources noted above
%%% have been corrected. Spelling has been
%%% verified with the UNIX spell and GNU ispell
%%% programs using the exception dictionary
%%% stored in the companion file with extension
%%% .sok.
%%%
%%% BibTeX citation tags are uniformly chosen as
%%% name:year:abbrev, where name is the family
%%% name of the first author or editor, year is a
%%% 4-digit number, and abbrev is a 3-letter
%%% condensation of important title
%%% words. Citation tags were automatically
%%% generated by software developed for the
%%% BibNet Project.
%%%
%%% This bibliography is sorted by year, and
%%% within each year, by author and title key,
%%% using ``bibsort -byyear''. Cross-referenced
%%% proceedings entries appear at the end,
%%% because of a restriction in the current
%%% BibTeX.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
%%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here.
%%% The more conventional undelimited form \toenglish{...} has braces
%%% that prevent BibTeX's downcasing operation, and the alternate form
%%% {\toenglish{...}} is considered a `special character' by BibTeX,
%%% and all of {...} gets downcased. We avoid the name \english to
%%% prevent conflicts with language options in packages like Babel.
%%%
%%% To suppress output of English translations of non-English titles,
%%% use
%%% "\def \toenglish #1\endtoenglish{\unskip}"
%%% instead.
%%%
%%% Alternative Cyrillic definitions are supplied in the event that
%%% cyracc.def is not loaded.
@Preamble{"\input bibnames.sty"
# "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} "
# "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"
# "\ifx \undefined \cyr \let \cyr = \relax \fi "
# "\ifx \undefined \cdprime \def \cdprime{''} \fi "
# "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi "
# "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}} \fi"
# "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi"
# "\hyphenation{ Rich-ard }"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.,
Santa Clara, CA 95054,
USA,
e-mail: \path|norbert@@iit.com|"}
@String{ack-rfb = "Ronald F. Boisvert,
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975 3812,
e-mail: \path=boisvert@cam.nist.gov="}
%%% ====================================================================
%%% Institution abbreviations:
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-BERKELEY-CS = "Department of Computer Science, University
of California"}
@String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"}
@String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics,
University of California, Berkeley"}
@String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"}
@String{inst-IPTC = "{Institut f{\"u}r Physikalische und
Theoretische Chemie}"}
@String{inst-IPTC:adr = "{Universit{\"a}t Regensburg, D-93040
Regensburg}"}
@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
Nancy-Brabois, 615 rue du jardin
botanique, F-54602
Villers-l{\`e}s-Nancy Cedex, France"}
@String{inst-MATH-NPS = "Department of Mathematics, Naval Postgraduate
School"}
@String{inst-MATH-NPS:adr = "Monterey CA 93943, USA"}
@String{inst-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, USA"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACTA-INFO = "Acta Informatica"}
@String{j-ACTA-MATH = "Acta Mathematica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ADV-APPL-MATH = "Advances in Applied Mathematics"}
@String{j-ADV-QUANTUM-CHEM = "Advances in Quantum Chemistry"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
Intelligence"}
@String{j-APPL-COMPUT-HARMON-ANAL = "Applied and Computational Harmonic
Analysis. Time-Frequency and
Time-Scale Analysis, Wavelets,
Numerical Algorithms, and
Applications"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics: Transactions
of IMACS"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-AUSTRALIAN-J-PHYS = "Australian Journal of Physics"}
@String{j-AUTOMATICA = "Automatica: the journal of IFAC, the
International Federation of Automatic
Control"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BRITISH-J-PHILOS-SCI = "British Journal for the Philosophy of
Science"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-CACM = "Communications of the ACM"}
@String{j-CALCOLO = "Calcolo"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics =
Journal canadien de
math{\'e}matiques"}
@String{j-CAN-MATH-BULL = "Bulletin canadien de
math\-{\'e}\-mat\-iques = Canadian
Mathematical Bulletin"}
@String{j-CCCUJ = "C/C++ Users Journal"}
@String{j-CELEST-MECH-DYN-ASTR = "Celestial Mechanics and Dynamical Astronomy"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-PHYSICS = "Computers in Physics"}
@String{j-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-COMPUT-MATH-MATH-PHYS = "Computational Mathematics and Mathematical
Physics"}
@String{j-COMPUT-PHYS-REP = "Computer Physics Reports"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing: Archiv fur informatik und
numerik"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-CONST-APPROX = "Constructive Approximation"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-EDN = "EDN"}
@String{j-ELECT-LETTERS = "Electronics Letters"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis (ETNA)"}
@String{j-ELECTRONIC-DESIGN = "Electronic Design"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"}
@String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"}
@String{j-EMBED-SYS-PROG = "Embedded Systems Programming"}
@String{j-EXP-MATH = "Experimental mathematics"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}
@String{j-HEWLETT-PACKARD-J = "Hew\-lett-Pack\-ard Journal: technical
information from the laboratories of
Hew\-lett-Pack\-ard Company"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"}
@String{j-IEEE-CGA = "IEEE Computer Graphics and Applications"}
@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
Systems. 2, Analog and Digital Signal
Processing"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-MICROWAVE-THEORY-TECH = "IEEE Transactions on Microwave
Theory and Techniques"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
Integration (VLSI) Systems"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IJSAHPC = "The International Journal of Supercomputer
Applications and High Performance Computing"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INT-J-COMPUT-INF-SCI = "International Journal of Computer and
Information Sciences"}
@String{j-INT-J-COMPUT-MATH = "International Journal of Computer
Mathematics"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical
education in science and technology"}
@String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and
Mathematical Sciences"}
@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-INTERNET-J-CHEM = "Internet Journal of Chemistry"}
@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
vychisleniia"}
@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}
@String{j-J-ACM = "Journal of the Association for Computing
Machinery"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMP-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPLEXITY = "Journal of complexity"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-GRAPHICS-GPU-GAME-TOOLS = "Journal of Graphics, GPU, and Game Tools"}
@String{j-J-HIGH-ENERGY-PHYS = "Journal of High Energy Physics"}
@String{j-J-INST-MATH-APPL = "Journal of the Institute of Mathematics and
its Applications"}
@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
Society = Chongbo Kwahakhoe nonmunji"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MOL-STRUCT-THEOCHEM = "Journal of Molecular Structure. Theochem"}
@String{j-J-MULTIVAR-ANAL = "Journal of Multivariate Analysis"}
@String{j-J-NUMER-METHODS-COMPUT-APPL = "Journal on Numerical Methods and
Computer Applications"}
@String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed
Computing"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and General)"}
@String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and
Simulation"}
@String{j-J-STAT-SOFT = "Journal of Statistical Software"}
@String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-J-SYMBOLIC-LOGIC = "Journal of Symbolic Logic"}
@String{j-J-UCS = "J.UCS: The Journal of Universal Computer Science"}
@String{j-J-VLSI-SIGNAL-PROC = "Journal of VLSI Signal Processing"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LIN-MULT-ALGEBRA = "Linear and Multilinear Algebra"}
@String{j-LMS-J-COMPUT-MATH = "LMS Journal of Computation and Mathematics"}
@String{j-LOGIN = ";login: the USENIX Association newsletter"}
@String{j-MATH-COMP-SIM = "Mathematics and Computers in Simulation"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-MODEL-NUM-ANA = "Mathematical modelling and numerical
analysis = Modelisation math{\'e}matique et
analyse num{\'e}rique: $M^2AN$"}
@String{j-MATH-OP-RES = "Mathematics of Operations Research"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to
Computation"}
@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
to Computation"}
@String{j-MATHEMATICA-J = "Mathematica Journal"}
@String{j-MICROPROC-MICROPROG = "Microprocessing and Microprogramming"}
@String{j-MICROPROC-MICROSYS = "Microprocessors and Microsystems"}
@String{j-NACH-ELEK = "Nachrichtentechnik Elektronik"}
@String{j-NEURAL-COMP = "Neural Computation"}
@String{j-NEURAL-NETWORKS = "Neural Networks"}
@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
informationsbehandling"}
@String{j-NOTRE-DAME-J-FORM-LOG = "Notre Dame Journal of Formal Logic"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUCL-INSTR-METH = "Nuclear Instruments and Methods"}
@String{j-NUCL-PHYS-B-PROC-SUPPL = "Nuclear Physics B, Proceedings Supplements"}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-OPER-RES = "Operations Research"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-PHIL-MAGAZINE = "Philosophical Magazine"}
@String{j-PHYS-REV-A = "Physical Review A"}
@String{j-PHYS-TODAY = "Physics Today"}
@String{j-PHYSICA-D = "Physica D"}
@String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical
Society"}
@String{j-PROC-IEEE = "Proceedings of the IEEE"}
@String{j-PROG-COMP-SOFT = "Programming and Computer Software;
translation of Programmirovaniye (Moscow,
USSR) Plenum"}
@String{j-PROGRAMMIROVANIE = "Programmirovanie"}
@String{j-RUSS-J-MATH-PHYS = "Russian Journal of Mathematical Physics"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-CONTROL-OPTIM = "SIAM Journal on Control and Optimization"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and
Applications"}
@String{j-SIAM-J-MATH-ANA = "SIAM journal on mathematical analysis"}
@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
Applied Mathematics: Series B, Numerical
Analysis"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-SIGADA-LETTERS = "ACM SIGADA Ada Letters"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGPLAN = "ACM SIGPLAN Notices"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special Interest Group
on Symbolic and Algebraic Manipulation)"}
@String{j-SPE = "Soft\-ware\emdash Prac\-tice and Experience"}
@String{j-STAT-PROB-LETT = "Statistics \& Probability Letters"}
@String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"}
@String{j-THEOR-COMP-SCI = "Theoretical Computer Science"}
@String{j-TOKYO-J-MATH = "Tokyo journal of mathematics"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{j-TRANS-AM-MATH-SOC = "Transactions of the American Mathematical
Society"}
@String{j-TRANS-INFO-PROCESSING-SOC-JAPAN = "Transactions of the Information
Processing Society of Japan"}
@String{j-TRANS-SOC-COMP-SIM = "Transactions of the Society for Computer
Simulation"}
@String{j-USSR-COMP-MATH-MATH-PHYS = "U.S.S.R. Computational Mathematics and
Mathematical Physics"}
@String{j-Z-ANAL-ANWEND = "Zeitschrift f{\"u}r Analysis und ihre
Anwendungen"}
@String{j-Z-MATH-LOGIK-GRUNDL-MATH = "Zeitschrift f{\"u}r mathematische
Logik und Grundlagen der Mathematik"}
%%% ====================================================================
%%% Publishers and their addresses:
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AFIPS = "AFIPS Press"}
@String{pub-AFIPS:adr = "Montvale, NJ, USA"}
@String{pub-A-K-PETERS = "A. K. Peters, Ltd."}
@String{pub-A-K-PETERS:adr = "Wellesley, MA, USA"}
@String{pub-AKADEMIE-VERLAG = "Akademie-Verlag"}
@String{pub-AKADEMIE-VERLAG:adr = "Berlin, Germany"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-BALTZER = "J. C. Baltzer AG, Scientific
Publishing Company"}
@String{pub-BALTZER:adr = "Basel, Switzerland"}
@String{pub-BENJAMIN = "W. A. {Benjamin, Inc.}"}
@String{pub-BENJAMIN:adr = "New York, NY, USA"}
@String{pub-BIRKHAUSER = "Birkh{\"a}user"}
@String{pub-BIRKHAUSER:adr = "Cambridge, MA, USA; Berlin, Germany; Basel,
Switzerland"}
@String{pub-CAMBRIDGE = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
@String{pub-CHAPMAN-HALL = "Chapman and Hall, Ltd."}
@String{pub-CHAPMAN-HALL:adr = "London, UK"}
@String{pub-CHAPMAN-HALL-CRC = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}
@String{pub-CLARENDON = "Clarendon Press"}
@String{pub-CLARENDON:adr = "Oxford, UK"}
@String{pub-CRC = "CRC Press"}
@String{pub-CRC:adr = "2000 N.W. Corporate Blvd., Boca Raton,
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@String{pub-ELSEVIER-ACADEMIC:adr = "Amsterdam, The Netherlands"}
@String{pub-ENH = "Elsevier North-Holland, Inc."}
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@String{pub-HRW:adr = "New York, NY, USA"}
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@String{pub-IEEE = "IEEE Computer Society Press"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver
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@String{pub-INTEL = "Intel Corporation"}
@String{pub-INTEL:adr = "Santa Clara, CA, USA"}
@String{pub-KLUWER = "Kluwer Academic Publishers"}
@String{pub-KLUWER:adr = "Dordrecht, The Netherlands"}
@String{pub-MCGRAW-HILL = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr = "New York, NY, USA"}
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@String{pub-NIST = "National Institute for Standards and Technology"}
@String{pub-NIST:adr = "Gaithersburg, MD, USA"}
@String{pub-NORTH-HOLLAND = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr = "Amsterdam, The Netherlands"}
@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PERGAMON = "Pergamon Press"}
@String{pub-PERGAMON:adr = "New York, NY, USA"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ, USA"}
@String{pub-PH = "Pren{\-}tice-Hall"}
@String{pub-PH:adr = "Englewood Cliffs, NJ 07632, USA"}
@String{pub-REK = "Robert E. Krieger Publishing Company"}
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@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
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@String{pub-SPIE:adr = "Bellingham, WA, USA"}
@String{pub-SPRINGER-WIEN = "Spring{\-}er"}
@String{pub-SPRINGER-WIEN:adr = "Wien / New York"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-TAYLOR-FRANCIS = "Taylor and Francis"}
@String{pub-TAYLOR-FRANCIS:adr = "Boca Raton, FL, USA"}
@String{pub-TEUBNER = "Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Leipzig"}
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@String{pub-USENIX:adr = "San Francisco, CA, USA"}
@String{pub-VIEWEG = "Friedrich Vieweg und Sohn"}
@String{pub-VIEWEG:adr = "Braunschweig, Germany"}
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@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128"}
%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNCS = "Lecture Notes in Computer Science"}
%%% ====================================================================
%%% Bibliography entries, sorted by year and citation label:
@Article{Ritt:1925:EFT,
author = "J. F. Ritt",
title = "Elementary functions and their inverses",
journal = j-TRANS-AM-MATH-SOC,
volume = "27",
number = "1",
pages = "68--90",
year = "1925",
CODEN = "TAMTAM",
ISSN = "0002-9947",
MRclass = "30A05 (33B10)",
MRnumber = "MR1501299",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
}
@Article{Dederick:1926:QDDc,
author = "L. S. Dederick",
title = "Questions and Discussions: Discussions: {A} Modified
Method for Cube Roots and Fifth Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "33",
number = "9",
pages = "469--472",
month = nov,
year = "1926",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:12 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "41",
number = "8",
pages = "504--506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb,
}
@Article{Airey:1937:CFA,
author = "J. R. Airey",
title = "The ``converging factor'' in asymptotic series and the
calculation of {Bessel}, {Laguerre} and other
functions",
journal = j-PHIL-MAGAZINE,
volume = "24",
number = "??",
pages = "521--552",
month = "????",
year = "1937",
CODEN = "PHMAA4",
ISSN = "0031-8086",
bibdate = "Thu Dec 01 14:26:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb,
}
@Book{Emde:1940:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
pages = "xii + 181",
year = "1940",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/45006177",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
}
@Article{Stoner:1941:FEF,
author = "Paul Matthew Stoner",
title = "Fitting the Exponential Function and the {Gompertz}
Function by the Method of Least Squares",
journal = j-J-AM-STAT-ASSOC,
volume = "36",
number = "216",
pages = "515--518",
month = dec,
year = "1941",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314095;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2278959",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{RCA:1943:TTF,
author = "{R. C. A.}",
title = "Tables of Trigonometric Functions in Non-Sexagesimal
Arguments",
journal = j-MATH-TABLES-AIDS-COMPUT,
volume = "1",
number = "2",
pages = "33--44",
month = apr,
year = "1943",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "Original journal has only `R. C. A.' as author:
possibly R. C. Archibald.",
acknowledgement = ack-nhfb,
}
@Article{Bateman:1944:GTB,
author = "Harry Bateman and Raymond Clare Archibald",
title = "A Guide to Tables of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "7",
pages = "205--308",
month = jul,
year = "1944",
CODEN = "MTTCAS",
ISSN = "0891-6837",
MRnumber = "6,132b",
MRreviewer = "G. Szeg{\"o}",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{DHL:1944:NCB,
author = "{D. H. L.}",
title = "Note on the Computation of the {Bessel} Function
${I}_n({X})$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "5",
pages = "133--135",
month = apr,
year = "1944",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "Original journal has only `D. H. L.' as author:
probably D. H. Lehmer.",
acknowledgement = ack-nhfb,
}
@Book{Lewis:1944:SCH,
author = "Charles J. Lewis",
title = "A survey of the confluent hypergeometric function",
publisher = "????",
address = "Washington, DC, USA",
pages = "155",
year = "1944",
LCCN = "QA351 .L53",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Abramowitz:1945:ZCB,
author = "Milton Abramowitz",
title = "Zeros of certain {Bessel} functions of fractional
order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "9",
pages = "353--354",
month = jan,
year = "1945",
CODEN = "MTTCAS",
ISSN = "0891-6837",
MRclass = "65.0X",
MRnumber = "6,132c",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Book{Emde:1945:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "Edwards Bros.",
address = "Ann Arbor, MI, USA",
pages = "xii + 181",
year = "1945",
LCCN = "????",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Original edition published in 1940.",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1946:MZC,
author = "Anonymous",
title = "More Zeros of Certain {Bessel} Functions of Fractional
Order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "118--119",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Book{Emde:1948:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
edition = "Second",
pages = "xii + 181",
year = "1948",
LCCN = "QA55 .E5 1948",
MRclass = "65.0X",
MRnumber = "11,263k",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Magnus:1949:FTS,
author = "Wilhelm Magnus and Fritz Oberhettinger",
title = "Formulas and theorems for the special functions of
mathematical physics",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
pages = "172",
year = "1949",
LCCN = "QA41 M19e",
bibdate = "Sat Oct 30 18:44:51 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the German by John Wermer.",
acknowledgement = ack-nhfb,
}
@Book{USNBSCL:1949:TCH,
author = "{United States National Bureau of Standards
Computation Laboratory }",
title = "Tables of the confluent hypergeometric function
{$F(n/2, 1/2, x)$ and related functions}",
volume = "3",
publisher = "US Government Printing Office",
address = "Washington, DC, USA",
pages = "xxii + 73",
year = "1949",
LCCN = "QA3 .U5 no. 3",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied mathematics series",
URL = "http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Mathematics; Tables",
}
@Article{Norlund:1950:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = "Mat. Tidsskr. B.",
volume = "1950",
number = "??",
pages = "18--21",
year = "1950",
MRclass = "33.0X",
MRnumber = "MR0045259 (13,554e)",
bibdate = "Thu Dec 01 12:41:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Danish",
}
@Article{Fogel:1951:FTE,
author = "{\`E}. K. Fogel'",
title = "A finite theory of elementary functions. {I}.
{Logarithmic} and exponential functions. ({Russian})",
journal = "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis",
volume = "5",
number = "46",
pages = "801--813",
year = "1951",
MRclass = "33.0X",
MRnumber = "15,218b",
MRreviewer = "H. N. Shapiro",
bibdate = "Sat Apr 25 13:05:19 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Salzer:1951:FCE,
author = "H. E. Salzer",
title = "Formulas for Calculating the Error Function of a
Complex Variable",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "67--70",
month = apr,
year = "1951",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Salzer:1951:RTT,
author = "H. E. Salzer",
title = "Radix Table for Trigonometric Functions and their
Inverses to High Accuracy",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "33",
pages = "9--11",
month = jan,
year = "1951",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@InBook{Goncarov:1952:EFC,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a complex variable",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "491--552",
year = "1952",
MRclass = "30.0X",
MRnumber = "14,1073c",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Goncarov:1952:EFR,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a real variable. Limits of
sequences and functions. {The} general concept of a
function",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "9--296",
year = "1952",
MRclass = "27.2X",
MRnumber = "14,1070d",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kuipers:1952:PSE,
author = "L. Kuipers",
title = "Properties of some elementary functions",
journal = "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
Math.",
volume = "55",
number = "14",
pages = "388--393",
year = "1952",
MRclass = "27.0X",
MRnumber = "14,360e",
MRreviewer = "E. Frank",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Scherberg:1953:ACP,
author = "Max G. Scherberg and John F. Riordan",
title = "Analogue Calculation of Polynomial and Trigonometric
Expansions (in {Other Aids to Computation})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "61--65",
month = jan,
year = "1953",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Atta:1954:CGH,
author = "Susie E. Atta and Ward C. Sangren",
title = "Calculation of Generalized Hypergeometric Series",
journal = j-J-ACM,
volume = "1",
number = "4",
pages = "170--172",
month = oct,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Tue Nov 08 21:50:00 1994",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jacm.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
}
@Article{Cahill:1954:PCH,
author = "W. F. Cahill",
title = "Programs for Computing the Hypergeometric Series (in
Automatic Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "45",
pages = "36--37",
month = jan,
year = "1954",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Clenshaw:1954:PAE,
author = "C. W. Clenshaw",
title = "Polynomial approximations to elementary functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
pages = "143--147",
year = "1954",
ISSN = "0891-6837",
MRclass = "41.1X",
MRnumber = "16,128f",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{LaFara:1954:MCI,
author = "Robert L. LaFara",
title = "A Method for Calculating Inverse Trigonometric
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "47",
pages = "132--139",
month = jul,
year = "1954",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Book{Hastings:1955:ADC,
author = "Cecil {Hastings, Jr.}",
title = "Approximations for digital computers",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 201",
year = "1955",
ISBN = "0-691-07914-5",
ISBN-13 = "978-0-691-07914-1",
LCCN = "QA76 .H37",
bibdate = "Mon Oct 01 15:59:48 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
series = "The Rand series",
acknowledgement = ack-nhfb,
remark = "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
fourth printing (1962).",
subject = "Electronic digital computers; Numerical analysis",
}
@Article{Norlund:1955:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = j-ACTA-MATH,
volume = "94",
number = "??",
pages = "289--349",
month = "????",
year = "1955",
CODEN = "ACMAA8",
DOI = "http://dx.doi.org/10.1007/BF02392494",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
MRclass = "33.0X",
MRnumber = "MR0074585 (17,610d)",
bibdate = "Thu Dec 01 10:09:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica",
}
@Article{Preston:1955:ACS,
author = "F. S. Preston",
title = "An Analog Computer for the Solution of Tangents",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "101--106",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/IRETELC.1955.5407908",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Robinson:1955:EAC,
author = "A. S. Robinson",
title = "An Electronic Analog Computing Technique for the
Solution of Trigonometric Problems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "95--101",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/IRETELC.1955.5407907",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Book{Sneddon:1956:SFM,
author = "Ian Naismith Sneddon",
title = "Special functions of mathematical physics and
chemistry",
volume = "19",
publisher = "Oliver and Boyd,",
address = "Edinburgh, UK",
edition = "Third",
pages = "viii + 164",
year = "1956",
LCCN = "QA1 U588 v. 19",
bibdate = "Sat Oct 30 18:41:48 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See second edition \cite{Sneddon:1961:SFM} and third
edition \cite{Sneddon:1980:SFM}.",
subject = "Functions, Special",
}
@Article{Hitchcock:1957:PAB,
author = "A. J. M. Hitchcock",
title = "Polynomial Approximations to {Bessel} Functions of
Order Zero and One and to Related Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "86--88",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of $e^{N}$ for $-\infty < {N} < +\infty$
Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "68.0X",
MRnumber = "19,775d",
bibdate = "Tue Sep 06 20:55:54 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
reviewer = "W. F. Freiberger",
}
@Article{Linskii:1957:CEF,
author = "V. S. Linski{\u{\i}}",
title = "Calculation of elementary functions on automatic
digital machines. ({Russian})",
journal = "Vy{\v{c}}isl. Mat.",
volume = "2",
pages = "90--119",
year = "1957",
MRclass = "68.00",
MRnumber = "21 \#982",
MRreviewer = "J. W. Carr, III",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Luke:1957:C,
author = "Yudell L. Luke",
title = "On the Computation of $\log {Z}$ and
$\operatorname{arc} \tan {Z}$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "57",
pages = "16--18",
month = jan,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Miller:1957:NGS,
author = "J. C. P. Miller",
title = "Note on the General Solution of the Confluent
Hypergeometric Equation",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "97--99",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Southard:1957:ATW,
author = "Thomas H. Southard",
title = "Approximation and Table of the {Weierstrass} $\wp$
Function in the Equianharmonic Case for Real Argument",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "99--100",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Stegun:1957:GBF,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Generation of {Bessel} Functions on High Speed
Computers",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "60",
pages = "255--257",
month = oct,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{T:1957:CHS,
author = "C. B. T.",
title = "Comment: {T. H. Southard, \booktitle{Approximation and
table of the Weierstrass $\wp$ function in the
equianharmonic case for real argument}. [MTAC, this
issue, p. 99--100]}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "110--110",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002157",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Beattie:1958:TFZ,
author = "Curtis L. Beattie",
title = "Table of First 700 Zeros of {Bessel} Functions ---
{$J_l(x)$} and {$J^{\prime}_l(x)$}",
journal = j-BELL-SYST-TECH-J,
volume = "37",
number = "3",
pages = "689--697",
month = may,
year = "1958",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.00",
MRnumber = "0093928 (20 \#448)",
MRreviewer = "J. C. P. Miller",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Book{Bowman:1958:IBF,
author = "Frank Bowman",
title = "Introduction to {Bessel} functions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 135",
year = "1958",
LCCN = "QA408 .B68i 1958",
bibdate = "Sat Jan 15 17:24:26 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "An unabridged and unaltered republication of the first
edition.",
subject = "Bessel functions",
}
@Article{Goldstein:1958:BFL,
author = "M. Goldstein and R. M. Thaler",
title = "{Bessel} Functions for Large Arguments",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "12",
number = "61",
pages = "18--26",
month = jan,
year = "1958",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {N} for $-\infty < {N} <
+\infty$ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "1",
pages = "43--53",
month = jan,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "65.3X",
MRnumber = "19,982e",
bibdate = "Wed Aug 31 13:40:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
reviewer = "C. B. Haselgrove",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {N} for $0<{N}<1$ Using an
Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "65.3X",
MRnumber = "19,1197c",
bibdate = "Wed Aug 31 13:41:37 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
reviewer = "C. B. Haselgrove",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Davis:1959:LEI,
author = "P. J. Davis",
title = "{Leonhard Euler}'s integral: {A} historical profile of
the gamma function: In Memoriam: {Milton Abramowitz}",
journal = j-AMER-MATH-MONTHLY,
volume = "66",
number = "10",
pages = "849--869",
month = dec,
year = "1959",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "00 (33.00)",
MRnumber = "MR0106810 (21 #5540)",
bibdate = "Mon Nov 24 20:57:26 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{DiDonato:1959:NFC,
author = "A. R. DiDonato and A. V. Hershey",
title = "New Formulas for Computing Incomplete Elliptic
Integrals of the First and Second Kind",
journal = j-J-ACM,
volume = "6",
number = "4",
pages = "515--526",
month = oct,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Mon Dec 05 20:10:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Emde:1959:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
edition = "Third",
pages = "xii + 181",
year = "1959",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/61020314",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
}
@Article{Goldstein:1959:RTC,
author = "M. Goldstein and R. M. Thaler",
title = "Recurrence Techniques for the Calculation of {Bessel}
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "66",
pages = "102--108",
month = apr,
year = "1959",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $\sin{N}$, $\cos{N}$, and ${M}$th Root
of ${N}$ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "65.00",
MRnumber = "21 \#964",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
reviewer = "B. A. Chartres",
}
@Article{Longman:1959:STT,
author = "I. M. Longman",
title = "A Short Table of $\int^\infty_x {J}_0(t)t^{-n} dt$ and
$\int^\infty_x {J}_1(t) t^{-n} dt$ (in {Technical Notes
and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "306--311",
month = oct,
year = "1959",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 6-digit values for $n = 1, 2, \ldots{}, 22$
and for $x = 1, 2, \ldots{}, 10$.",
}
@Article{Luke:1959:ECH,
author = "Yudell L. Luke",
title = "Expansion of the Confluent Hypergeometric Function in
Series of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "261--271",
month = oct,
year = "1959",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
}
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sherry:1959:CGF,
author = "M. E. Sherry and S. Fulda",
title = "Calculation of Gamma Functions to High Accuracy (in
{Technical Notes and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "314--315",
month = oct,
year = "1959",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compj.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
}
@Article{Volder:1959:CCT,
author = "Jack Volder",
title = "The {CORDIC} Computing Technique",
journal = "Proceedings of the Western Joint Computer Conference",
pages = "257--261",
year = "1959",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Beam:1960:ACE,
author = "A. Beam",
title = "{Algorithm 14}: {Complex} exponential integral",
journal = j-CACM,
volume = "3",
number = "7",
pages = "406--406",
month = jul,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: 30-line Algol procedure incorrectly
labelled algorithm 13.",
}
@Article{Haimovici:1960:MRE,
author = "Corina Haimovici",
title = "A method of representing elementary functions in
algebras of finite order. ({Romanian})",
journal = "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
Sec{\c{t}} I. (N.S.)",
volume = "6",
pages = "507--515",
year = "1960",
MRclass = "26.00",
MRnumber = "24 \#A1342",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Harumi:1960:VTN,
author = "Kasaburo Harumi and Shigetoshi Katsura and John W.
{Wrench, Jr.}",
title = "Values of {$\frac{2}{\pi} \int^\infty_0
\Big(\frac{\sin t}{t}\Big)^n dt$} (in {Technical Notes
and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "72",
pages = "379--379",
month = oct,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 10-digit table for $n = 1, 2, \ldots{},
30$.",
}
@InCollection{Kogbetliantz:1960:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of elementary functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1960",
MRclass = "68.00 (65.00)",
MRnumber = "22 \#8681",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lang:1960:ECC,
author = "H. A. Lang",
title = "On the Evaluation of Certain Complex Elliptic
Integrals (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "195--199",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Manual{Maehly:1960:ACD,
author = "Hans J. Maehly",
title = "Approximations for the {Control Data 1604}",
organization = "Institute for Advanced Study",
address = "Princeton, NJ",
pages = "ii + 44",
day = "15",
month = jan,
year = "1960",
bibdate = "Tue Nov 06 00:39:07 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
acknowledgement = ack-nhfb,
keywords = "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
$\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}
@Article{Philip:1960:FI,
author = "J. R. Philip",
title = "The function $\operatorname{inverfc} \theta$",
journal = j-AUSTRALIAN-J-PHYS,
volume = "13",
number = "1",
pages = "13--20",
month = mar,
year = "1960",
CODEN = "AUJPAS",
ISSN = "0004-9506",
MRnumber = "22 \9626",
bibdate = "Tue Sep 11 20:53:59 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The function inverfc $\theta$ arises in certain
differential equations when concentration is taken as
an independent variable. It enters into a general
method of exact solution of the concentration-dependent
diffusion equation. An account is given of the
properties of this function, and of its derivatives and
integrals. The function\par
$$B(\theta) = (2/\pi^{1/2})
\exp[-(\operatorname{inverfc} \theta)^2]$$
\noindent is intimately connected with the first
integral of inverfc $\theta$ and with its derivatives.
Tables of $\operatorname{inverfc} \theta$ and
$B(\theta)$ are given.",
acknowledgement = ack-nhfb,
ZMnumber = "135.28302",
}
@Book{Rainville:1960:SF,
author = "Earl David Rainville",
title = "Special Functions",
publisher = "Chelsea Publishing Company",
address = "New York, NY, USA",
pages = "xii + 365",
year = "1960",
ISBN = "0-8284-0258-2",
ISBN-13 = "978-0-8284-0258-3",
LCCN = "QA331 R15; QA351 .R3 1971",
bibdate = "Mon Sep 3 16:04:28 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1971.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Based upon the lectures on special functions which
\ldots{} [the author has] been giving at the University
of Michigan since 1946. Fullerton: All traditional
functions and polynomials are discussed in some
detail.",
subject = "Functions, Special",
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Sholander:1960:AEE,
author = "Marlow Sholander",
title = "Analytical expressions and elementary functions",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
pages = "213--214",
year = "1960",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26.00",
MRnumber = "22 \#9553",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Slater:1960:CHF,
author = "Lucy Joan Slater",
title = "Confluent hypergeometric functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "247",
year = "1960",
LCCN = "QA351 .S56",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Discussion of properties and 7 decimal
place tables of $_1F_1(a;b;x)$.",
subject = "Hypergeometric functions",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Book{Warmus:1960:TEF,
author = "Mieczys{\l}aw Warmus",
title = "Tables of elementary functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "vii + 567",
year = "1960",
LCCN = "QA55 .W3 1960",
MRclass = "65.05",
MRnumber = "23 \#B1141",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately
bound table of proportional parts, 30 pp.",
acknowledgement = ack-nhfb,
}
@Article{Barakat:1961:EIG,
author = "Richard Barakat",
title = "Evaluation of the Incomplete Gamma Function of
Imaginary Argument by {Chebyshev} Polynomials",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "7--11",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Boersma:1961:TFR,
author = "J. Boersma",
title = "Two Formulas Relating to Elliptic Integrals of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "296--298",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Corrington:1961:ACE,
author = "Murlan S. Corrington",
title = "Applications of the Complex Exponential Integral",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "1--6",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Ehrling:1961:NCI,
author = "G. Ehrling",
title = "On the Numerical Computation of Incomplete Elliptic
Integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "1",
pages = "8--14",
month = mar,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01961946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:06 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8",
acknowledgement = ack-nhfb,
}
@Article{Fields:1961:EHF,
author = "Jerry L. Fields and Jet Wimp",
title = "Expansions of Hypergeometric Functions in
Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "390--395",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Froberg:1961:RCA,
author = "Carl-Erik Fr{\"o}berg",
title = "Rational {Chebyshev} Approximations of Elementary
Functions",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "4",
pages = "256--262",
month = dec,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933243",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Froberg:1963:ERC}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Gautschi:1961:RCR,
author = "Walter Gautschi",
title = "Recursive Computation of the Repeated Integrals of the
Error Function",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "227--232",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Herndon:1961:ABF,
author = "John R. Herndon",
title = "{Algorithm 57}: {Ber} or {Bei} Function",
journal = j-CACM,
volume = "4",
number = "4",
pages = "181--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: 20-line Algol procedure that only sums
series.",
}
@Article{Herndon:1961:ACEa,
author = "John R. Herndon",
title = "{Algorithm 55}: {Complete} elliptic integral of the
first kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--180",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Herndon:1961:ACEb,
author = "John R. Herndon",
title = "{Algorithm 56}: {Complete} elliptic integral of the
second kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Book{Hochstadt:1961:SFM,
author = "Harry Hochstadt",
title = "Special functions of mathematical physics",
publisher = pub-HRW,
address = pub-HRW:adr,
pages = "viii + 81",
year = "1961",
ISBN = "0-236-73011-8",
ISBN-13 = "978-0-236-73011-7",
LCCN = "QA351 H65 1961",
bibdate = "Sat Oct 30 18:01:08 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted 1966.",
}
@Article{Landau:1961:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {II}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "65--84",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140733 (25 \#4147)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Luke:1961:EHF,
author = "Yudell L. Luke and Richard L. Coleman",
title = "Expansion of Hypergeometric Functions in Series of
Other Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "233--237",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Rader:1961:CAC,
author = "P. J. Rader and Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 14 [not 13]}: {Complex}
exponential integral",
journal = j-CACM,
volume = "4",
number = "2",
pages = "105--105",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:30 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: It's accurate but sometimes slow.",
}
@Article{Slepian:1961:PSW,
author = "D. Slepian and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {I}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "43--63",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140732 (25 \#4146)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Book{Sneddon:1961:SFM,
author = "Ian Naismith Sneddon",
title = "Special functions of mathematical physics and
chemistry",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
edition = "Ssecond",
pages = "184",
year = "1961",
LCCN = "QA331 .S65 1961",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See first edition \cite{Sneddon:1956:SFM} and third
edition {Sneddon:1980:SFM}",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.20",
MRnumber = "MR0134842 (24 \#B894)",
MRreviewer = "M. E. Rose",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Werner:1961:CAG,
author = "Helmut Werner and Robert Collinge",
title = "{Chebyshev} Approximations to the Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "195--197",
month = apr,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Albrecht:1962:FKM,
author = "J. Albrecht",
title = "{Fehlerschranken und Konvergenzbeschleunigung bei
einer monotonen oder alternierenden Iterationsfolge}.
({German}) [{Error} Bounds and Convergence Acceleration
with a Monotone or Alternating Iteration Sequence]",
journal = j-NUM-MATH,
volume = "4",
pages = "196--208",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "German",
}
@TechReport{Blanch:1962:TRR,
author = "Gertrude Blanch and Donald S. Clemm",
title = "Tables Relating to the Radial {Mathieu} Functions,
Vols. 1 \& 2",
type = "Report",
institution = "Aeronautical Research Labs. U. S. Government Printing
Office",
address = "Washington, DC, USA",
year = "1962",
bibdate = "Fri Oct 29 21:37:53 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Gertrude Blanch (1897--1996)",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 7-place tables.",
}
@Article{Boersma:1962:CLF,
author = "J. Boersma",
title = "On the Computation of {Lommel}'s Functions of Two
Variables (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "232--238",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Lommel's functions are infinite sums
involving Bessel functions $J_{\nu - 2m}(x)$.",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Christiansen:1962:APC,
author = "S{\o}ren Christiansen",
title = "{Algol} Programming: Contribution no. 3: Calculation
of complementary {Fresnel} integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "3",
pages = "192--194",
year = "1962",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:34:20 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: A 50-line Algol procedure is given. It
calculates $\int_x^\infty \cos(t)/\sqrt{2 \pi t} \, dt$
and $\int_x^\infty \sin(t)/\sqrt{2 \pi t} \, dt$.",
}
@Article{Cundiff:1962:AEA,
author = "John L. Cundiff",
title = "{Algorithm 88}: {Evaluation} of Asymptotic Expression
for the {Fresnel} Sine and Cosine Integrals",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Can be used with algorithms 89 and 90.
30-line Algol procedure.",
}
@Article{Cundiff:1962:AEFa,
author = "John L. Cundiff",
title = "{Algorithm 89}: {Evaluation} of the {Fresnel} Sine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "S(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{Cundiff:1962:AEFb,
author = "John L. Cundiff",
title = "{Algorithm 90}: {Evaluation} of the {Fresnel} Cosine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "281--281",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "C(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{Hansen:1962:SRV,
author = "Eldon R. Hansen and Merrell L. Patrick",
title = "Some Relations and Values for the Generalized
{Riemann} Zeta Function",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "265--274",
month = jul,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Jefferson:1962:RAI,
author = "David K. Jefferson",
title = "Remark on {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "5",
number = "10",
pages = "514--514",
month = oct,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:41 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Landau:1962:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {III}. {The} dimension of the space of
essentially time- and band-limited signals",
journal = j-BELL-SYST-TECH-J,
volume = "41",
number = "4",
pages = "1295--1336",
month = jul,
year = "1962",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28 (94.10)",
MRnumber = "0147686 (26 \#5200)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Merner:1962:AAC,
author = "J. N. Merner",
title = "{ACM Algorithm 149}: Complete Elliptic Integral",
journal = j-CACM,
volume = "5",
number = "12",
pages = "605",
month = dec,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 09:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Skovgaard:1978:RCE}.",
acknowledgement = ack-nhfb,
}
@Article{Thacher:1962:CAB,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 57}:
{$\operatorname{ber}$} or {$\operatorname{bei}$}
function",
journal = j-CACM,
volume = "5",
number = "8",
pages = "438--438",
month = aug,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: The algorithm is inaccurate for large
$x$.",
}
@Article{Thacher:1962:CAH,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithms 191 and 192,
Hypergeometric and Confluent Hypergeometric
Functions}",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1962",
bibdate = "Sat Oct 30 11:27:28 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: An error in a comment is noted.",
}
@Article{Burgoyne:1963:AKF,
author = "F. D. Burgoyne",
title = "Approximations to {Kelvin} Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "17",
number = "83",
pages = "295--298",
month = jul,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 9-digit approximations.",
}
@Article{Carlitz:1963:IEF,
author = "L. Carlitz",
title = "The Inverse of the Error Function",
journal = j-PAC-J-MATH,
volume = "13",
number = "2",
pages = "459--470",
year = "1963",
CODEN = "PJMAAI",
ISSN = "0030-8730",
bibdate = "Thu Sep 13 21:30:05 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://pjm.math.berkeley.edu/pjm;
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
acknowledgement = ack-nhfb,
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: ALGOL 60 procedures with accuracy $\approx
10^{-15}$ for $\exp$, $\ln$, $\sin$, $\cos$, $\tan$,
$\arcsin$, $\arctan$, $\gamma$, $\Ei$ and $\erf$. See
G. F. Miller (1965) for corrections.",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
of square roots",
journal = j-COMP-J,
volume = "6",
number = "3",
pages = "274--276",
month = oct,
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:49 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/compj.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/060274.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/tiff/274.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/tiff/275.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/tiff/276.tif",
acknowledgement = ack-nhfb # " and " # ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Fettis:1963:AMH,
author = "Henry E. Fettis",
title = "{Algorithm 163}: {Modified} {Hankel} function",
journal = j-CACM,
volume = "6",
number = "4",
pages = "161--162",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Hankel functions; special functions",
remark = "Fullerton: A 25-line Algol procedure for $e^x
K_p(x)$.",
}
@Article{Froberg:1963:APC,
author = "Carl-Erik Fr{\"o}berg",
title = "{Algol} Programming: Contribution no. 5: Computation
of the {Fermi} function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "2",
pages = "141--142",
year = "1963",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The Fermi function depends on several
physical parameters of the atomic nucleus.",
}
@Article{Froberg:1963:ERC,
author = "C.-E. Fr{\"o}berg",
title = "Erratum: {``Rational Chebyshev Approximations of
Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
line 12]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "1",
pages = "68--68",
month = mar,
year = "1963",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01963538",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Froberg:1961:RCA}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Gray:1963:AFI,
author = "Malcolm D. Gray",
title = "{Algorithm 213}: {Fresnel} Integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "617--617",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Gray:1964:CAF} and related
remark \cite{Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
keywords = "C(x); S(x); special functions",
}
@Article{Gray:1963:RAE,
author = "Malcolm D. Gray",
title = "Remark on Algorithms 88, 89, and 90 evaluation of the
{Fresnel} integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "618--618",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: An error is noted.",
}
@Article{Hofsommer:1963:NCE,
author = "D. J. Hofsommer and R. van de Riet",
title = "On the numerical calculation of elliptic integrals of
the first and second kind and the elliptic functions of
{Jacobi}",
journal = j-NUM-MATH,
volume = "5",
pages = "291--302",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lee-Whiting:1963:EFC,
author = "G. E. Lee-Whiting",
title = "Erratum: ``{Formulas} for Computing Incomplete
Elliptic Integrals of the First and Second Kinds''",
journal = j-J-ACM,
volume = "10",
pages = "412--412",
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Sat Dec 10 15:59:26 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Lee-Whiting:1963:FCI}.",
acknowledgement = ack-nhfb,
xxmonth = "none",
xxnumber = "none",
}
@Article{Lee-Whiting:1963:FCI,
author = "G. E. Lee-Whiting",
title = "Formulas for Computing Incomplete Elliptic Integrals
of the First and Second Kinds",
journal = j-J-ACM,
volume = "10",
number = "2",
pages = "126--130",
month = apr,
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Sat Nov 05 22:55:28 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Lee-Whiting:1963:EFC}.",
acknowledgement = ack-nhfb,
}
@Book{Ljusternik:1963:MVF,
author = "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
Janpol{\'s}ki{{\u{\i}}}",
title = "{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
{\`e}lementarnykh funktsi{\u{\i}}}. [Mathematical
analysis. {Computation} of the elementary functions]",
publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.",
address = "Moscow, USSR",
pages = "247",
year = "1963",
MRclass = "65.25",
MRnumber = "28 \#1733",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ludwig:1963:AIB,
author = "Oliver G. Ludwig",
title = "{Algorithm 179}: {Incomplete} beta ratio",
journal = j-CACM,
volume = "6",
number = "6",
pages = "314--314",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: This algorithm is the basis for a modern
treatment by Bosten and Battiste.",
}
@Article{Meyer:1963:CAI,
author = "Noelle A. Meyer",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "2",
pages = "69--69",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:44 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Newman:1963:ICS,
author = "J. N. Newman and W. Frank",
title = "An Integral Containing the Square of a {Bessel}
Function",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "64--70",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The integral $I_n^m(x) = \int_0^{\pi/2}
\frac{J_n^2(x \cos (\theta))}{(x \cos(\theta))^{2m}} \,
d\theta$, where $m$ and $n$ are either integers or half
integers, is considered.",
}
@Article{Peuizulaev:1963:AEF,
author = "{\v{S}}. I. Pe{\u{\i}}zulaev",
title = "An approximation by elementary functions.
({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "3",
pages = "769--770",
year = "1963",
MRclass = "41.30",
MRnumber = "28 \#398",
MRreviewer = "D. D. Stancu",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Relph:1963:AAH,
author = "A. P. Relph",
title = "{ACM Algorithm 191}: Hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--389",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:32:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
}
@Article{Relph:1963:ACH,
author = "A. P. Relph",
title = "{Algorithm 192}: {Confluent} hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 30-line Algol procedure for complex args.
The work of Luke supersedes this.",
}
@Article{Relph:1963:AH,
author = "A. P. Relph",
title = "{Algorithm 191}: {Hypergeometric}",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 30-line Algol procedure. The work of Luke
is better.",
}
@Book{Sneddon:1963:SFM,
author = "Ian Naismith Sneddon",
title = "{Spezielle Funktionen der mathematischen Physik und
Chemie. Mathematische Formelsammlung II}. ({German})
[Special {functions} of mathematical physics and
chemistry. {Mathematical} formula collection {II}]",
volume = "54",
publisher = "Bibliographisches Institut",
address = "Mannheim, West Germany",
pages = "166",
year = "1963",
LCCN = "QA351 .S6415",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "B. I.-Hochschultaschenb{\"u}cher",
acknowledgement = ack-nhfb,
language = "German",
remark = "German translation of \cite{Sneddon:1961:SFM}.",
subject = "Functions; Mathematical physics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Sweeney:1963:CEC,
author = "Dura W. Sweeney",
title = "On the Computation of {Euler}'s Constant",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "170--178",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 3566 digits should be enough.",
}
@Article{Thacher:1963:ACEa,
author = "Henry C. {Thacher, Jr.}",
title = "{Algorithm 165}: {Complete} elliptic integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "163--164",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Thacher:1963:CACa,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 55}: {Complete} elliptic
integral of the first kind",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Thacher:1963:CACb,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 149}: {Complete} elliptic
integral",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{vandeRiet:1963:CAI,
author = "R. P. van de Riet",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "167--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Werner:1963:AFI,
author = "H. Werner and G. Raymann",
title = "An Approximation to the {Fermi} Integral
${F}_{1/2}(x)$",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "193--194",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors of $5 \times 10^{-4}$.",
}
@Article{Whittlesey:1963:IGF,
author = "John R. B. Whittlesey",
title = "Incomplete Gamma Functions for Evaluating {Erlang}
Process Probabilities",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "11--17",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@InCollection{Abramowitz:1964:CWF,
author = "Milton Abramowitz",
title = "{Coulomb} Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "537--554",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Abramowitz:1964:SFR,
author = "Milton Abramowitz",
title = "{Struve} Functions and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "495--502",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Antosiewicz:1964:BFF,
author = "H. A. Antosiewicz",
title = "{Bessel} Functions of Fractional Order",
crossref = "Abramowitz:1964:HMF",
pages = "435--478",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Blanch:1964:MF,
author = "Gertrude Blanch",
title = "{Mathieu} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "721--750",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1897--1996",
citedby = "Fullerton:1980:BEM",
}
@Article{Bray:1964:CAGa,
author = "T. A. Bray",
title = "Certification of {Algorithm 225}: {Gamma} function
with controlled accuracy",
journal = j-CACM,
volume = "7",
number = "10",
pages = "586--586",
month = oct,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: No corrections were necessary.",
}
@Article{Burgoyne:1964:GTF,
author = "F. D. Burgoyne",
title = "Generalized Trigonometric Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "314--316",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Cody:1964:DPS,
author = "William J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
keywords = "$sqrt(x)$; CDC 3600; elementary functions;
floating-point arithmetic",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Curtiss:1964:EIB,
author = "C. F. Curtiss",
title = "Expansions of Integrals of {Bessel} Functions of Large
Order",
journal = j-J-MATH-PHYS,
volume = "5",
number = "4",
pages = "561--564",
month = apr,
year = "1964",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1704149",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:12 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1",
acknowledgement = ack-nhfb,
onlinedate = "22 December 2004",
pagecount = "4",
}
@Article{Cyvin:1964:AGF,
author = "S. J. Cyvin and B. N. Cyvin",
title = "{Algorithm 225}: {Gamma} function with controlled
accuracy",
journal = j-CACM,
volume = "7",
number = "5",
pages = "295--295",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: 30-line Algol procedure based on
out-of-date method.",
}
@InCollection{Davis:1964:GFR,
author = "Philip J. Davis",
title = "Gamma Function and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "253--294",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@TechReport{Fisherkeller:1964:TCE,
author = "M. A. Fisherkeller and W. J. {Cody, Jr.}",
title = "Tables of the Complete Elliptic Integrals ${K}$,
${K}'$, ${E}$, and ${E}'$",
type = "Technical Memo",
number = "ANL AMD 71",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "14",
year = "1964",
bibdate = "Thu Nov 17 10:44:21 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See review by John W. Wrench in Mathematics of
Computation, {\bf 19}(89--92), 342, 1965.",
acknowledgement = ack-nhfb,
}
@Article{Gargantini:1964:RCA,
author = "I. Gargantini and T. Pomentale",
title = "Rational {Chebyshev} approximations to the {Bessel}
function integrals {$Ki_s(x)$}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "727--730",
month = dec,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "65.25",
MRnumber = "31\#863",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The second Remes algorithm is used to approximate the
integrals $Ki_s$ by rational functions. The related
coefficients for the approximations of $Ki_1, Ki_2,
Ki_3$ are given for different precisions.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Bessel functions; Kis(x); special functions",
remark = "Fullerton: Approximations for repeated integrals
$\operatorname{Ki}_s(x)$ of $K(x)$ for $s= 1, 2, 3$ are
given for accuracies down to $10^{-5}$ for $s = 1$ and
to $10^{-7}$ for $s = 2, 3$.",
}
@Article{Gautschi:1964:AIB,
author = "Walter Gautschi",
title = "{Algorithm 222}: {Incomplete} beta functions ratios",
journal = j-CACM,
volume = "7",
number = "3",
pages = "143--143",
month = mar,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:52 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "beta functions; special functions",
remark = "Fullerton: 200-line Algol procedure.",
}
@Article{Gautschi:1964:CAI,
author = "Walter Gautschi",
title = "Certification of {Algorithm 222}: {Incomplete} beta
function ratios",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "beta functions; special functions",
remark = "Fullerton: A typographical error is noted.",
}
@InCollection{Gautschi:1964:EFF,
author = "Walter Gautschi",
title = "Error Function and {Fresnel} Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "295--330",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Gautschi:1964:EIR,
author = "Walter Gautschi and William F. Cahill",
title = "Exponential Integral and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "227--252",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Gray:1964:CAF,
author = "Malcolm Gray",
title = "Certification of {Algorithm 213}: {Fresnel}
integrals",
journal = j-CACM,
volume = "7",
number = "11",
pages = "661--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gray:1963:AFI,Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Several corrections are given.",
}
@InCollection{Haynsworth:1964:BEP,
author = "Emilie V. Haynsworth and Karl Goldberg",
title = "{Bernoulli} and {Euler} Polynomials, {Riemann Zeta}
Function",
crossref = "Abramowitz:1964:HMF",
pages = "803--820",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Hochstrasser:1964:OP,
author = "Urs W. Hochstrasser",
title = "Orthogonal Polynomials",
crossref = "Abramowitz:1964:HMF",
pages = "771--802",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Hummer:1964:EDF,
author = "David G. Hummer",
title = "Expansions of {Dawson}'s Function in a Series of
{Chebyshev} Polynomials (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "317--319",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Almost l5-digit approximations.",
}
@Article{Lanczos:1964:PAG,
author = "C. Lanczos",
title = "A Precision Approximation of the Gamma Function",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "??",
pages = "86--96",
month = "????",
year = "1964",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2949767",
acknowledgement = ack-nhfb,
}
@Article{Lotsch:1964:AFI,
author = "Helmut Lotsch and Malcolm Gray",
title = "{Algorithm 244}: {Fresnel} Integrals [{S20}]",
journal = j-CACM,
volume = "7",
number = "11",
pages = "660--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This procedure computes the Fresnel sine and cosine
integrals $C(w) = \int_0^\infty \cos [(\pi/2)t^2]\,dt$
and $S(w) = \int_0^w \sin [(\pi/2)t^2]\,dt$. It is a
modification of Algorithm 213 (Comm. ACM, 6 (Oct.
1963), 617) such that the accuracy, expressed by
\textit{eps}, is improved. eps can arbitrarily be
chosen up to $\textit{eps} = 10^{-6}$ for a computer
with sufficient word length as, for example, the
Burroughs B5000 which has 11--12 significant digits.
Referring to the formulas of Algorithm 213: if $|w| <
\sqrt{(26.20/\pi)}$ the series expansions $C(w)$ and
$S(w)$ are terminated when the absolute value of the
relative change in two successive terms is $\leq
\textit{eps}$. If $|w| \geq \sqrt{(26.20/\pi)}$ the
series $Q(x)$ and $P(x)$ are terminated when the
absolute value of the terms is $\leq \textit{eps}/2$.
However, this truncation point is not necessarily valid
for the range $\sqrt{(26.20/\pi)} \leq |w| <
\sqrt{(28.50/\pi)}$ when $\textit{eps} = 10^{-6}$,
since the asymptotic series must be terminated before
arriving at the minimum. In this range the ignored
terms of the series expansions are $< 3 \times 10^{6}$,
and for larger arguments $< 10^{-6}$. This accuracy may
be improved if desired: the switch-over point from the
regular to the asymptotic series expansions has to be
displaced to larger arguments.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "C(x); Fresnel integrals; S(x); special functions",
remark = "Fullerton: 100-line Algol procedure.",
}
@InCollection{Lowan:1964:SWF,
author = "Arnold N. Lowan",
title = "Spheroidal Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "751--770",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Luke:1964:IBF,
author = "Yudell L. Luke",
title = "Integrals of {Bessel} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "479--494",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Miller:1964:PCF,
author = "J. C. P. Miller",
title = "Parabolic Cylinder Functions",
crossref = "Abramowitz:1964:HMF",
pages = "685--720",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:EI,
author = "L. M. Milne-Thomson",
title = "Elliptic Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "587--626",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:JEF,
author = "L. M. Milne-Thomson",
title = "{Jacobian} Elliptic Functions and Theta Functions",
crossref = "Abramowitz:1964:HMF",
pages = "567--586",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Morelock:1964:AAE,
author = "J. C. Morelock",
title = "{ACM} Algorithm 229: Elementary Functions by Continued
Fractions",
journal = j-CACM,
volume = "7",
number = "5",
pages = "296",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 09:32:21 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Oberhettinger:1964:HF,
author = "Frtiz Oberhettinger",
title = "Hypergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "555--566",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Olver:1964:BFI,
author = "F. W. J. Olver",
title = "{Bessel} Functions of Integer Order",
crossref = "Abramowitz:1964:HMF",
pages = "355--434",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Schmidt:1964:AEC,
author = "Paul W. Schmidt",
title = "Asymptotic Expansion of Certain Integrals Containing
the {Bessel} Function {$J_0(x)$}",
journal = j-J-MATH-PHYS,
volume = "5",
number = "8",
pages = "1183--1184",
month = aug,
year = "1964",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1704223",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:15 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1",
acknowledgement = ack-nhfb,
onlinedate = "22 December 2004",
pagecount = "2",
}
@Article{Simauti:1964:AFS,
author = "Takakazu Simauti",
title = "Approximation formulas for some elementary functions",
journal = "Comment. Math. Univ. St. Paul.",
volume = "12",
pages = "23--35",
year = "1964",
CODEN = "COMAAC",
ISSN = "0010-258X",
MRclass = "65.25",
MRnumber = "28 \#5552",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Slater:1964:CHF,
author = "Lucy Joan Slater",
title = "Confluent Hvpergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "503--536",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Slepian:1964:PSW,
author = "David Slepian",
title = "Prolate Spheroidal Wave Functions, {Fourier} Analysis
and Uncertainty --- {IV}: Extensions to Many
Dimensions; Generalized Prolate Spheroidal Functions",
journal = j-BELL-SYST-TECH-J,
volume = "43",
number = "6",
pages = "3009--3057",
month = nov,
year = "1964",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28",
MRnumber = "0181766 (31 \#5993)",
MRreviewer = "J. Meixner",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@InCollection{Southard:1964:WER,
author = "Thomas H. Southard",
title = "{Weierstrass} Elliptic and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "627--684",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:LF,
author = "Irene A. Stegun",
title = "{Legendre} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "331--354",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:MF,
author = "Irene A. Stegun",
title = "Miscellaneous Functions",
crossref = "Abramowitz:1964:HMF",
pages = "997--1010",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Clausen's integral; Clebsch--Gordan coefficients;
Debye function; Dilogarithm (Spence's integral);
Einstein function; Planck function; Sievert and related
integrals",
remark = "Fullerton: Debye, Planck and Einstein functions.
Sievert and related integrals. Dilogarithm (Spence's
integral). Clausen's integral. Clebsch--Gordan
coefficients.",
}
@Article{Wengert:1964:SAD,
author = "R. E. Wengert",
title = "A simple automatic derivative evaluation program",
journal = j-CACM,
volume = "7",
number = "8",
pages = "463--464",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A procedure for automatic evaluation of total and
partial derivatives of arbitrary algebraic functions is
presented. The numerical values of derivatives are
computed without developing analytic expressions for
the derivatives. The function is decomposed into a
sequence of elementary expressions A library is
provided for differentiating of elementary functions.",
acknowledgement = ack-nhfb,
keywords = "computer program.; differentiation arithmetic; point
algorithm",
referred = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
[Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
[Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
[Wilk64a].",
}
@InCollection{Zelen:1964:PF,
author = "Marvin Zelen and Norman C. Severo",
title = "Probability Functions",
crossref = "Abramowitz:1964:HMF",
pages = "925--996",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Zucker:1964:ETF,
author = "Ruth Zucker",
title = "Elementary Transcendental Functions. {Logarithmic},
Exponential, Circular and Hyperbolic Functions",
crossref = "Abramowitz:1964:HMF",
pages = "65--226",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bingulac:1965:ACG,
author = "S. P. Bingulac and E. A. Humo",
title = "Analog Computer Generation of {Bessel} Functions of
Arbitrary Order",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "886--889",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264084",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Braess:1965:MIG,
author = "Dietrich Braess",
title = "{Monotone Iterationsfolgen bei Gleichungssystemen mit
fehlerhaften Koeffizienten und
Iterationsbeschleunigung}. ({German}) [{Monotone}
Iteration Sequences for Equation Systems with
Coefficients Having Errors, and Iteration
Acceleration]",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "32--41",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "German",
}
@Article{Bulirsch:1965:NCEa,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "78--90",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Handbook Series Special functions",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bulirsch:1965:NCEb,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {II}",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "353--354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Christiansen:1965:APE,
author = "S. Christiansen",
title = "{Algol} programming: Error Integral with Complex
Argument",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "287--293",
month = dec,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01937509",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: A 75-line Algol procedure with maximum
absolute error about $2 \times 10^{-6}$ is given for
$w(z) = e^{-z^2} \erfc(-iz)$.",
}
@Article{Cochran:1965:ZHF,
author = "J. A. Cochran",
title = "The zeros of {Hankel} functions as functions of their
order",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "238--250",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 10:06:00 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Cody:1965:CAC,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Approximations for the Complete Elliptic
Integrals {$K$} and {$E$}",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "105--112",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.05",
MRnumber = "30\#1601",
bibdate = "Fri Oct 23 11:10:16 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1966:CCA}.",
URL = "http://www.jstor.org/stable/2004103",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors down to $4 \times
10^{-18}$.",
}
@Article{Cody:1965:CPE,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Polynomial Expansions of Complete Elliptic
Integrals",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "249--259",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.25",
MRnumber = "31\#2820",
bibdate = "Fri Oct 23 11:10:33 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2003350",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 25-digit approximations.",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dahlquist:1965:CAP,
author = "Germund Dahlquist and Sven-{\AA}ke Gustafson and
K{\'a}roly Sikl{\'o}si",
title = "Convergence Acceleration from the Point of View of
Linear Programming",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "1--16",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01975719",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Fettis:1965:CEI,
author = "Henry E. Fettis",
title = "Calculation of Elliptic Integrals of the Third Kind by
Means of {Gauss}' Transformation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "97--104",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004102",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fields:1965:RAG,
author = "Jerry L. Fields",
title = "Rational Approximations to Generalized Hypergeometric
Functions",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "606--624",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Franke:1965:NEE,
author = "Charles H. Franke",
title = "Numerical Evaluation of the Elliptic Integral of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "494--496",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fraser:1965:SMC,
author = "W. Fraser",
title = "A Survey of Methods for Computing Minimax and
Near-Minimax Polynomial Approximations for Functions of
a Single Independent Variable",
journal = j-J-ACM,
volume = "12",
number = "3",
pages = "295--314",
month = jul,
year = "1965",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/321281.321282",
ISSN = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Methods are described for the derivation of minimax
and near-minimax polynomial approximations. For minimax
approximations techniques are considered for both
analytically defined functions and functions defined by
a table of values. For near-minimax approximations
methods of determining the coefficients of the
Fourier--Chebyshev expansion are first described. These
consist of the rearrangement of the coefficients of a
power polynomial, and also direct determination of the
coefficients from the integral which defines them, or
the differential equation which defines the function.
Finally there is given a convenient modification of an
interpolation scheme which finds coefficients of a
near-minimax approximation without requiring numerical
integration or the numerical solution of a system of
equations.",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1965:ALF,
author = "W. Gautschi",
title = "{Algorithm 259}: {Legendre} Functions for Arguments
Larger than One [{S16}]",
journal = j-CACM,
volume = "8",
number = "8",
pages = "488--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Jansen:1977:RLF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Legendre functions; special functions",
remark = "Fullerton: Long Algol procedures for the associated
Legendre functions of the first and second kinds:
$P_a^n(x)$ and $Q_n^m$.",
}
@Article{Gunn:1965:ASa,
author = "J. H. Gunn",
title = "{Algorithm 260}: {6-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:ASb,
author = "J. H. Gunn",
title = "{Algorithm 261}: {9-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--493",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:AZV,
author = "J. H. Gunn",
title = "{Algorithm 252} [{Z}]: {Vector} coupling or
{Clebsch--Gordan} coefficients",
journal = j-CACM,
volume = "8",
number = "4",
pages = "217--217",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:59 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Heatley:1965:ETT,
author = "A. H. Heatley",
title = "An Extension of the Table of the {Toronto} Function
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "118--123",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Some 5 and 7-digit values.",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Article{Kazangapov:1965:REF,
author = "A. N. Kazangapov",
title = "Representation of elementary function in the system of
residual classes. ({Russian})",
journal = "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
volume = "3",
pages = "79--84",
year = "1965",
MRclass = "65.25",
MRnumber = "33 \#5090",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpol{\'s}kii",
title = "Handbook for Computing Elementary Functions",
volume = "76",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
MRclass = "65.25",
MRnumber = "32 \#584",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
series = "International series of monographs on pure and applied
mathematics",
acknowledgement = ack-nhfb,
}
@Article{Maklovic:1965:IIC,
author = "S. T. Maklovi{\v{c}}",
title = "Investigation of integrals containing {Bessel} and
elementary functions. ({Russian})",
journal = "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
volume = "82",
pages = "75--81",
year = "1965",
MRclass = "33.25",
MRnumber = "34 \#387",
MRreviewer = "H. A. Lauwerier",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Markman:1965:RZF,
author = "B. Markman",
title = "The {Riemann} Zeta Function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "2",
pages = "138--141",
year = "1965",
bibdate = "Sat Oct 30 08:53:17 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: A 25-line Algol procedure for evaluating
$\zeta(s)$ for all $s \neq 1$ is given.",
}
@Article{Medhurst:1965:EI,
author = "R. G. Medhurst and J. H. Roberts",
title = "Evaluation of the Integral ${I}_n(b) = \frac{2}{\pi}
\int^\infty_0 \bigg(\frac{\sin x}{x}\bigg)^n \cos (bx)
dx$",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "113--117",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Corrections and simplifications of the
$\sin$, $\cos$ and $\tan$ routines given in paper I.
See Clenshaw (1963).",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Nemeth:1965:CEF,
author = "G. N{\'e}meth",
title = "{Chebyshev} expansions for {Fresnel} integrals",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "310--312",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Two series of 12-digit coefficients are
given to cover the range $0 <= x < \infty$.",
}
@Article{Slepian:1965:EAP,
author = "David Slepian and Estelle Sonnenblick",
title = "Eigenvalues associated with prolate spheroidal wave
functions of zero order",
journal = j-BELL-SYST-TECH-J,
volume = "44",
number = "8",
pages = "1745--1759",
month = oct,
year = "1965",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.25",
MRnumber = "0183103 (32 \#585)",
MRreviewer = "R. Nicolovius",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Slepian:1965:SAE,
author = "David Slepian",
title = "Some Asymptotic Expansions for Prolate Spheroidal Wave
Functions",
journal = "J. Math. and Physics {XLIV(2)}",
volume = "??",
number = "??",
pages = "99--140",
month = jun,
year = "1965",
bibdate = "Sat Oct 30 10:46:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661",
acknowledgement = ack-nhfb,
author-dates = "1923--2007",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Several complicated expansions are derived
and presented.",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Thompson:1965:AEI,
author = "G. T. Thompson",
title = "The Asymptotic Expansion of the Integrals Psi and Chi
in Terms of {Tchebycheff} Polynomials (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "661--663",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Doppler Broadening",
}
@Article{Cody:1966:CCA,
author = "W. J. {Cody, Jr.}",
title = "Corrigenda: ``{Chebyshev} Approximations for the
Complete Elliptic Integrals ${K}$ and ${E}$''",
journal = j-MATH-COMPUT,
volume = "20",
number = "93",
pages = "207--207",
month = jan,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Fri Oct 23 11:13:58 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1965:CAC}.",
acknowledgement = ack-nhfb,
}
@Article{Doring:1966:CZC,
author = "Boro Doring",
title = "Complex Zeros of Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "215--222",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM System\slash 360}",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:05 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the {Richardson}
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "2",
pages = "127--132",
month = jun,
year = "1966",
CODEN = "CMPTA2",
DOI = "http://dx.doi.org/10.1007/BF02342622",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Gautschi:1966:AD,
author = "Walter Gautschi",
title = "{Algorithm 282}: {Derivatives} of $e^x/x$,
$\cos(x)/x$, and $\sin(x)/x$",
journal = j-CACM,
volume = "9",
number = "4",
pages = "272--272",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:05 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Gautschi:1970:RAD}.",
acknowledgement = ack-nhfb,
keywords = "$\cos(x)/x$; $\sin(x)/x$; $e^x/x$; elementary
functions",
}
@Article{Gautschi:1966:ARC,
author = "Walter Gautschi",
title = "{Algorithm 292}: {Regular} {Coulomb} Wave Functions",
journal = j-CACM,
volume = "9",
number = "11",
pages = "793--795",
month = nov,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:10 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
}
@Article{Glasser:1966:ESI,
author = "M. L. Glasser",
title = "Evaluation of Some Integrals Involving the
$\psi$-Function (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "332--333",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Gustafson:1966:CAM,
author = "Sven-{\AA}ke Gustafson",
title = "Convergence Acceleration by Means of Numerical
Quadrature",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "2",
pages = "117--128",
month = jun,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933103",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Hastings:1966:RCB,
author = "C. W. Hastings",
title = "{R66-78} Computation of the Base Two Logarithm of
Binary Number",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "6",
pages = "956--957",
month = dec,
year = "1966",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1966.264517",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:46 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Jurimae:1966:KFT,
author = "E. J{\"u}rim{\"a}e",
title = "Kompleksmuutuja funktsioonide teooria. {I}:
Elementaarsed funktsioonid. ({Estonian}) [Theory of
functions of a complex variable. {I}: Elementary
functions]",
publisher = "Tartu Riiklik {\"U}likool",
address = "Tartu, Estonia",
pages = "131",
year = "1966",
MRclass = "30.00",
MRnumber = "40 \#5827a",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@TechReport{Kuki:1966:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
type = "????",
number = "SSD 169, C4773",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "47--53",
year = "1966",
bibdate = "Wed Feb 14 19:13:50 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Larssen:1966:CAC,
author = "Gerhard Meidell Larssen",
title = "Certification of {Algorithm 56}: {Complete} elliptic
integral of the second kind",
journal = j-CACM,
volume = "9",
number = "1",
pages = "12--12",
month = jan,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Book{Magnus:1966:FTS,
author = "Wilhelm Magnus and Fritz Oberhettinger and Raj Pal
Soni",
title = "Formulas and theorems for the special functions of
mathematical physics",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "viii + 508",
year = "1966",
LCCN = "QA1 G88 v. 52, 1966",
bibdate = "Sat Oct 30 18:23:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Mechel:1966:CMB,
author = "Fr. Mechel",
title = "Calculation of the Modified {Bessel} Functions of the
Second Kind with Complex Argument",
journal = j-MATH-COMPUT,
volume = "20",
number = "95",
pages = "407--412",
month = jul,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Nellis:1966:REE,
author = "W. J. Nellis and B. C. Carlson",
title = "Reduction and Evaluation of Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "223--231",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Pike:1966:ALG,
author = "M. C. Pike and I. D. Hill",
title = "{Algorithm 291}: {Logarithm} of Gamma Function",
journal = j-CACM,
volume = "9",
number = "9",
pages = "684--684",
month = sep,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:09 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\log(\Gamma(x))$; special functions",
remark = "Fullerton: Short Algol procedure valid only for $x >
0$. Accurate to 10 digits.",
}
@Book{Slater:1966:GHF,
author = "Lucy Joan Slater",
title = "Generalized hypergeometric functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 273",
year = "1966",
LCCN = "QA351 .S565",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Takenaga:1966:EIG,
author = "Roy Takenaga",
title = "On the Evaluation of the Incomplete Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "606--610",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Thompson:1966:ESI,
author = "Rory Thompson",
title = "Evaluation of ${I}_n(b) = 2\pi^{-1} \int^\infty_0
\big(\frac{sin x}{x}\big) ^n \cos (bx) dx$ and of
Similar Integrals (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "330--332",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Wood:1966:DBI,
author = "Van E. Wood and R. P. Kenan and M. L. Glasser",
title = "{Doppler} Broadening Integrals (in {Technical Notes
and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "610--611",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Anonymous:1967:CAP,
author = "Anonymous",
title = "Convergence acceleration from the point of view of
linear programming",
journal = j-BIT,
volume = "7",
number = "3",
pages = "256--256",
month = sep,
year = "1967",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01939269",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:10 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Bond:1967:AAF,
author = "Gillian Bond and M. L. V. Pitteway",
title = "{Algorithm 301}: {Airy} Function",
journal = j-CACM,
volume = "10",
number = "5",
pages = "291--292",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Airy functions; special functions",
remark = "Fullerton: 100-line Algol program for
$\operatorname{Ai}$, $\operatorname{Bi}$. and their
derivatives.",
}
@Article{Cody:1967:CAN,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the Natural Logarithm
of the Gamma Function",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "198--203",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors down to $10^{-17}$.",
}
@Article{Cody:1967:CRC,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Corrigendum: ``{Rational Chebyshev approximations for
Fermi--Dirac integrals of orders $-1/2$, $1/2$, and
$3/2$''}",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "525--525",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Mon Sep 26 19:36:03 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1967:RCA}.",
URL = "http://www.jstor.org/stable/2003289",
acknowledgement = ack-nhfb,
xxmonth = "(none)",
}
@Article{Cody:1967:RCA,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for {Fermi--Dirac}
integrals of orders $-1/2$, $1/2$, and $3/2$",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "30--40",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Mon Sep 26 19:23:19 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1967:CRC}.",
URL = "http://www.jstor.org/stable/2003468",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors down to $10^{-9}$.",
}
@Article{DiDonato:1967:ECI,
author = "A. R. DiDonato and M. P. Jarnagin",
title = "The Efficient Calculation of the Incomplete
Beta-Function Ratio for Half-Integer Values of the
Parameters $a, b$",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "652--662",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fair:1967:RAI,
author = "Wyman G. Fair and Yudell L. Luke",
title = "Rational Approximations to the Incomplete Elliptic
Integrals of the First and Second Kinds",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "418--422",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fettis:1967:MCI,
author = "Henry E. Fettis",
title = "More on the Calculation of the Integral ${I}_n(b) =
\frac{2}{\pi}\int^\infty_0\big(\frac{\sin x}{x}\big)^n
\cos bx dx$ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "727--730",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Fike:1967:LER,
author = "C. T. Fike",
title = "Letter to the {Editor}: {A} rational approximation
optimal by {Moursund}'s criterion",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:16 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
acknowledgement = ack-nhfb,
keywords = "elementary function; square root",
remark = "Gives a starting value for $\sqrt{x}$ ($x$ on
$[1/16,1]$) of $R*(x) = 1.68212586 - 1.28977371 / (x +
0.84106293)$, with an error of $2^{-12.496}$.",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "http://dx.doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Gunn:1967:ACW,
author = "J. H. Gunn",
title = "{Algorithm 300}: {Coulomb} Wave Functions",
journal = j-CACM,
volume = "10",
number = "4",
pages = "244--245",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Vos:1973:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: 150-line Algol procedure that is superceded
by other routines in the physics literature.",
}
@Article{Hill:1967:ACS,
author = "I. D. Hill and M. C. Pike",
title = "{Algorithm 299}: {Chi}-Squared Integral",
journal = j-CACM,
volume = "10",
number = "4",
pages = "243--244",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Hill:1967:ANCa,
author = "I. D. Hill and S. A. Joyce",
title = "{Algorithm 304}: {Normal} Curve Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "374--375",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "{\tt normal(x,upper)} calculates the curve, i.e., tail
area of the standardized normal curve, i.e.,
$(1/\sqrt{2\pi})\int \exp(-t^2/2)\,dt$. If {\tt upper}
is {\tt true}, the limits of integration are $x$ and
$\infty$. If {\tt upper} is {\tt false}, the limits of
integration are $-\infty$ and $x$.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "probability functions",
remark = "Fullerton: 75-line Algol procedure that is superceded
by numerous $\erf$ routines.",
}
@Article{Hill:1967:RAS,
author = "I. D. Hill and S. A. Joyce",
title = "Remarks on {Algorithm 123} [{S15}]: {Real} error
function, {\tt ERF(x)}; {Algorithm 180} [{S15}]:
{Error} Function --- Large ${X}$; {Algorithm 181}
[{S15}]: {Complementary} Error Function --- Large
${X}$; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm
226} [{S15}]: {Normal} Distribution Function;
{Algorithm 272} [{S15}]: {Procedure} for the Normal
Distribution Functions; {Algorithm 304} [{S15}]:
{Normal} Curve Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "377--378",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "$\erf(x)$; $\erfc(x)$; probability functions; special
functions",
}
@Article{Kilpatrick:1967:CIP,
author = "J. E. Kilpatrick and Shigetoshi Katsura and Yuji
Inoue",
title = "Calculations of Integrals of Products of {Bessel}
Functions",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "407--412",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Knuth:1967:CTE,
author = "Donald E. Knuth and Thomas J. Buckholtz",
title = "Computation of Tangent, {Euler}, and {Bernoulli}
Numbers",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "663--688",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.25",
MRnumber = "36 #4787",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The first 119. 120 and 250 tangent, Euler
and Bernoulli numbers, respectively.",
}
@Book{MacRobert:1967:SHE,
author = "Thomas Murray MacRobert and Ian Naismith Sneddon",
title = "Spherical harmonics; an elementary treatise on
harmonic functions, with applications",
volume = "98",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
edition = "Third",
pages = "xviii + 349",
year = "1967",
LCCN = "QA406 .M3 1967",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "International series of monographs in pure and applied
mathematics",
acknowledgement = ack-nhfb,
author-dates = "1884--1962",
subject = "Spherical harmonics",
}
@Article{Moody:1967:ADF,
author = "William T. Moody",
title = "Approximations for the Psi (Digamma) Function (in
Technical Notes and Short Notices)",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "112--112",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Moursund:1967:OSV,
author = "David G. Moursund",
title = "Optimal starting values for {Newton--Raphson}
calculation of $\sqrt{x}$",
journal = j-CACM,
volume = "10",
number = "7",
pages = "430--432",
month = jul,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "39\#2297",
bibdate = "Fri Nov 25 18:20:14 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See letter \cite{Fike:1967:LER}.",
acknowledgement = ack-nhfb,
keywords = "$sqrt(x)$; elementary functions",
remark = "Title of article has incorrect $\sqrt(x^{1/2})$: the
article discusses computation of {\tt sqrt(x)}.",
}
@Article{Olver:1967:BSS,
author = "F. W. J. Olver",
title = "Bounds for the Solutions of Second-Order Linear
Difference Equations [{Anger--Weber} and {Struve}
Functions]",
journal = "J. Res. Nat. Bur. Stand.",
volume = "71B",
number = "4",
pages = "161--166",
month = oct,
year = "1967",
bibdate = "Sat Oct 30 09:37:44 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards",
remark = "Fullerton: Truncation error estimates of an earlier
published algorithm.",
}
@Article{Pike:1967:RAI,
author = "M. C. Pike and I. D. Hill",
title = "Remark on {Algorithm 179}: {Incomplete} {Beta} ratio",
journal = j-CACM,
volume = "10",
number = "6",
pages = "375--376",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$B(z,w)$; beta function; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Pitteway:1967:RAA,
author = "M. L. V. Pitteway",
title = "Remark on {Algorithm 301}: {Airy} function",
journal = j-CACM,
volume = "10",
number = "7",
pages = "453--453",
month = jul,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:14 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Airy functions; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Book{Sen:1967:TSF,
author = "Bibhutibhusan Sen",
title = "A treatise on special functions, for scientists and
engineers",
publisher = "Allied Publishers",
address = "Bombay, India",
pages = "164",
year = "1967",
LCCN = "QA351 .S45",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Spherical harmonics",
}
@Article{Verma:1967:NSG,
author = "Arun Verma",
title = "A Note on the Summation of the Generalised
Hypergeometric Functions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "232--236",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Wood:1967:CEI,
author = "Van E. Wood",
title = "{Chebyshev} Expansions for Integrals of the Error
Function (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "494--496",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 7-digit approximations for $i^n \erfc(x), n
= 1, 2$.",
}
@Article{Anonymous:1968:ISA,
author = "Anonymous",
title = "Index by Subject to Algorithms, 1960--1968",
journal = j-CACM,
volume = "11",
number = "12",
pages = "827--830",
month = dec,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sat Oct 30 09:29:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Arsenin:1968:BES,
author = "V. Ja. (Vasilii Jakovlevich) Arsenin",
title = "Basic equations and special functions of mathematical
physics",
publisher = "Iliffe",
address = "London, UK",
pages = "7 + 361",
year = "1968",
ISBN = "0-592-05035-1",
ISBN-13 = "978-0-592-05035-5",
LCCN = "QC20 .A693",
bibdate = "Sat Oct 30 18:25:22 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by S. Chomet, Kings College, London of
Matematicheska{\"e}i{\`\i}a fizika.",
acknowledgement = ack-nhfb,
subject = "Mathematical physics",
}
@Book{Bell:1968:SFS,
author = "W. W. (William Wallace) Bell",
title = "Special functions for scientists and engineers",
publisher = "Van Nostrand",
address = "London, UK",
pages = "xiv + 247",
year = "1968",
LCCN = "QA351 .B4",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Gamma, Beta, Legendre, Bessel, and
Hypergeometric functions as well as orthogonal
polynomials. Reprinted in \cite{Bell:2004:SFS}.",
subject = "Functions, Special",
}
@Article{Bergson:1968:ACR,
author = "A. Bergson",
title = "Certification of and remark on {Algorithm 304}
[{S15}]: {Normal} curve integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "probability functions",
remark = "Fullerton: 50-line Algol Program that is superceded by
numerous {\tt erf} routines.",
}
@Article{Bingulac:1968:RAA,
author = "S. P. Bingulac",
title = "{R68-38} Accurate Analog Computer Generation of
{Bessel} Functions for Large Ranges",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "8",
pages = "819--819",
month = aug,
year = "1968",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1968.229133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Chiarella:1968:EIR,
author = "C. Chiarella and A. Reichel",
title = "On the Evaluation of Integrals Related to the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "137--143",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Cody:1968:RCAa,
author = "W. J. Cody and H. C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for the
exponential integral {$E_1(x)$}",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "641--649",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.25",
MRnumber = "38\#6745",
bibdate = "Wed Jan 17 08:57:34 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors down to $10^{-21}$.",
}
@Article{Dorrer:1968:ADS,
author = "Egon Dorrer",
title = "{Algorithm 322}: {$F$}-Distribution [{S14}]",
journal = j-CACM,
volume = "11",
number = "2",
pages = "116--117",
month = feb,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:18 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 50-line Algol Program.",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Fleckner:1968:MCF,
author = "Oscar L. Fleckner",
title = "A Method for the Computation of the {Fresnel}
Integrals and Related Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "635--640",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Galant:1968:HAG,
author = "D. C. Galant and P. F. Byrd",
title = "High Accuracy Gamma Function Values for Some Rational
Arguments (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "104",
pages = "885--887",
month = oct,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-REK,
address = pub-REK:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "????",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Luke:1968:AEI,
author = "Yudell L. Luke",
title = "Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "627--634",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Mavromatis:1968:IFP,
author = "H. A. Mavromatis and K. Schilcher",
title = "Inverse Functions of the Products of Two {Bessel}
Functions and Applications to Potential Scattering",
journal = j-J-MATH-PHYS,
volume = "9",
number = "10",
pages = "1627--1632",
month = oct,
year = "1968",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1664492",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:17 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1",
acknowledgement = ack-nhfb,
classification = "A0380 (General theory of scattering)",
corpsource = "Dept. Physics, American Univ. Beirut, Lebanon",
keywords = "functions; mathematics; scattering",
onlinedate = "28 October 2003",
pagecount = "6",
}
@Article{Mechel:1968:IRT,
author = "Fr. Mechel",
title = "Improvement in Recurrence Techniques for the
Computation of {Bessel} Functions of Integral Order (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "202--205",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Miller:1968:LTS,
author = "Willard Miller",
title = "{Lie} theory and special functions",
volume = "43",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 338",
year = "1968",
ISBN = "0-12-497450-3",
ISBN-13 = "978-0-12-497450-0",
LCCN = "QA387 .M55 1968eb",
bibdate = "Sat Oct 30 19:07:04 MDT 2010",
bibsource = "catalog.library.cornell.edu:7090/voyager;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in science and engineering",
acknowledgement = ack-nhfb,
remark = "Reprinted 1979 with same ISBN.",
subject = "Lie groups; Functions, Special",
}
@Article{Nagashima:1968:EFN,
author = "Takashi Nagashima",
title = "On elementary functions of natural numbers",
journal = "Hitotsubashi J. Arts Sci.",
volume = "9",
pages = "50--58",
year = "1968",
ISSN = "0073-2788",
MRclass = "02.72",
MRnumber = "MR0232678 (38 \#1001)",
MRreviewer = "R. L. Goodstein",
bibdate = "Mon Oct 24 11:33:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Hitotsubashi Journal of Arts \& Sciences",
}
@Article{Ng:1968:DSS,
author = "Edward W. Ng",
title = "On the direct summation of series involving higher
transcendental functions",
journal = j-J-COMPUT-PHYS,
volume = "3",
number = "2",
pages = "334--338",
month = oct,
year = "1968",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(68)90029-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Dec 31 07:21:24 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999168900296",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{OBrien:1968:CAC,
author = "William M. O'Brien and Joan Wood",
title = "Certification of {Algorithm 299} [{S15}]:
{Chi-squared} integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Osborn:1968:IBF,
author = "David Osborn and Richard Madey",
title = "The Incomplete Beta Function and its Ratio to the
Complete Beta Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "159--162",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Richardson:1968:SUP,
author = "Daniel Richardson",
title = "Some Undecidable Problems Involving Elementary
Functions of a Real Variable",
journal = j-J-SYMBOLIC-LOGIC,
volume = "33",
number = "4",
pages = "514--520",
month = dec,
year = "1968",
CODEN = "JSYLA6",
ISSN = "0022-4812",
MRclass = "02.75",
MRnumber = "39 #1330",
bibdate = "Mon May 19 13:04:20 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Schmidt:1968:AEK,
author = "Jochen W. Schmidt",
title = "{Asymptotische Einschlie{\ss}ung bei
konvergenzbeschleunigenden Verfahren. II}. ({German})
[{Asymptotic enclosure with convergence acceleration
method. II}]",
journal = j-NUM-MATH,
volume = "11",
number = "1",
pages = "53--56",
month = jan,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "German",
}
@Article{Strecok:1968:CIE,
author = "Anthony J. Strecok",
title = "On the Calculation of the Inverse of the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "144--158",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004772",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 18-digit approximations.",
}
@Book{Talman:1968:SFG,
author = "James D. Talman",
title = "Special Functions: {A} Group Theoretic Approach Based
on Lectures by {Eugene P. Wigner}",
publisher = pub-BENJAMIN,
address = pub-BENJAMIN:adr,
pages = "xii + 260",
year = "1968",
LCCN = "????",
bibdate = "Sat Oct 30 16:57:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "With an introduction by Eugene P. Wigner.",
series = "The mathematical physics monograph series",
acknowledgement = ack-nhfb,
keywords = "group theory; mathematical function; special
functions",
}
@Article{Tooper:1968:SCP,
author = "Robert F. Tooper and John Mark",
title = "Simplified Calculation of {$\operatorname{Ei}(x)$} for
Positive Arguments, and a Short Table of
$\operatorname{Shi}(x)$ (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "448--449",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "exponential integral ($\operatorname{Ei}(x)$);
hyperbolic sine integral ($\operatorname{Shi}(x)$)",
}
@Article{Wilcox:1968:ZTN,
author = "Peter H. Wilcox",
title = "The Zeros of ${P}^1_\nu (\cos \theta)$ and
$\frac{\partial}{\partial \theta} {P}^1_\mu (\cos
\theta)$ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "205--208",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004783",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: $P_\nu^1$ are Legendre functions.",
}
@Article{Wimp:1968:RFH,
author = "Jet Wimp",
title = "Recursion Formulae of Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "363--373",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Witte:1968:AAJ,
author = "B. F. W. Witte",
title = "{ACM Algorithm 332}: {Jacobi} Polynomials",
journal = j-CACM,
volume = "11",
number = "6",
pages = "436--437",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 09:33:08 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Skovgaard:1975:RAJ}.",
acknowledgement = ack-nhfb,
}
@Article{Wrench:1968:CTS,
author = "John W. {Wrench, Jr.}",
title = "Concerning Two Series for the Gamma Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "617--626",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRnumber = "MR 0237078 (38:5371)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Aharoni:1969:C,
author = "Amikam Aharoni",
title = "Computation of {$K_p(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "2",
pages = "270--271",
month = aug,
year = "1969",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(69)90072-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 08:28:03 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999169900722",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Boersma:1969:ECW,
author = "J. Boersma",
title = "Expansions for {Coulomb} Wave Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "51--59",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Buchholz:1969:CHF,
author = "Herbert Buchholz",
title = "The confluent hypergeometric function with special
emphasis on its applications",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 238",
year = "1969",
LCCN = "QA351 .B813",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by H. Lichtblau and K. Wetzel to English
from German ``Die konfluente hypergeometrische
Funktion.''",
series = "Springer tracts in natural philosophy",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Bulirsch:1969:EBT,
author = "R. Bulirsch",
title = "An extension of the {Bartky}-transformation to
incomplete elliptic integrals of the third kind",
journal = j-NUM-MATH,
volume = "13",
number = "3",
pages = "266--284",
month = jul,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bulirsch:1969:NCE,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {III}",
journal = j-NUM-MATH,
volume = "13",
number = "4",
pages = "305--315",
month = aug,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Carlson:1969:CBE,
author = "B. C. Carlson",
title = "A connection between elementary functions and higher
transcendental functions",
journal = j-SIAM-J-APPL-MATH,
volume = "17",
pages = "116--148",
year = "1969",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
MRclass = "33.20 (30.00)",
MRnumber = "40 \#408",
MRreviewer = "S. K. Bose",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
pages = "701--706",
year = "1969",
bibdate = "Wed Sep 07 10:49:33 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Clemm:1969:ACV,
author = "Donald S. Clemm",
title = "{Algorithm 352}: {Characteristic} Values and
Associated Solutions of {Mathieu}'s Differential
Equation [{S22}]",
journal = j-CACM,
volume = "12",
number = "7",
pages = "399--407",
month = jul,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4170 (Differential equations); C7300 (Natural
sciences computing)",
corpsource = "Wright-Patterson Air Force Base, USA",
keywords = "differential equations; function evaluation;
subroutines",
remark = "Fullerton: Long set of FORTRAN routines to evaluate
Mathieu functions as well as several Bessel
functions.",
}
@Article{Cobb:1969:CAS,
author = "S. M. Cobb",
title = "Certification of {Algorithm 47} [{S16}]: {Associated}
{Legendre} functions of the first kind for real or
imaginary arguments",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--636",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "associated Legendre functions of the first kind;
special functions",
remark = "Fullerton: Numerous additional corrections and changes
to an Algol procedure.",
}
@Article{Cody:1969:CAE,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Exponential
Integral {$\hbox{Ei}(x)$}",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "289--303",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.25",
MRnumber = "39\#3680",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Cody:1969:CRA,
author = "W. J. Cody and G. Meinardus and R. S. Varga",
title = "{Chebyshev} rational approximations to $e^{-x}$ on
$[0,\infty)$ and applications to heat conduction
problems",
journal = j-J-APPROX-THEORY,
volume = "2",
number = "??",
pages = "50--65",
month = "??",
year = "1969",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
MRclass = "65.67 (41.00)",
MRnumber = "40\#999",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
}
@Article{Farkas:1969:CAS,
author = "I. Farkas",
title = "Certification of {Algorithm 165} [{S21}]: {Complete}
elliptic integrals",
journal = j-CACM,
volume = "12",
number = "1",
pages = "38--38",
month = jan,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "special functions",
}
@Article{Gautschi:1969:ACE,
author = "Walter Gautschi",
title = "{Algorithm 363}: {Complex} Error Function [{S15}]",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--635",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Kolbig:1972:CAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "$\erf(z)$; special functions",
remark = "Fullerton: 50-line Algol procedure with accuracy to 10
decimal places.",
}
@Article{Gautschi:1969:RAS,
author = "Walter Gautschi",
title = "Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "280--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Herman:1969:NHE,
author = "G. T. Herman",
title = "A new hierarchy of elementary functions",
journal = j-PROC-AM-MATH-SOC,
volume = "20",
pages = "557--562",
year = "1969",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "02.77",
MRnumber = "40 \#4110",
MRreviewer = "G. E. Sacks",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion}. ({German}) {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function}",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
month = jun,
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing",
language = "German",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kolbig:1969:CASa,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 292} [{S22}]: {Regular}
{Coulomb} wave functions and of remark on {Algorithm
292} [{S22}]: {Regular} {Coulomb} wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "278--279",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: Tests of an Algol procedure.",
}
@Article{Kolbig:1969:CASb,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 300} [{S22}]: {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "279--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Kolbig:1969:RAS,
author = "K. S. K{\"o}lbig",
title = "Remark on {Algorithm 300} [{S22}]: {Coulomb} wave
functions",
journal = j-CACM,
volume = "12",
number = "12",
pages = "692--692",
month = dec,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: One of many remarks.",
}
@Article{Lewis:1969:FII,
author = "Richard L. Lewis",
title = "On Finite Integrals Involving Trigonometric, {Bessel},
and {Legendre} Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "259--273",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Book{Luke:1969:SFTa,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "I",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 349",
year = "1969",
ISBN = "0-12-459901-X",
ISBN-13 = "978-0-12-459901-7",
LCCN = "QA351 .L94 1969",
bibdate = "Wed Dec 15 17:55:35 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering, Volume 53-I,
Editor: Richard Bellman",
acknowledgement = ack-nhfb,
}
@Book{Luke:1969:SFTb,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "II",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 485",
year = "1969",
ISBN = "0-12-459902-8",
ISBN-13 = "978-0-12-459902-4",
LCCN = "QA351 .L797",
bibdate = "Wed Dec 15 17:55:38 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering, Volume 53-II,
Editor: Richard Bellman",
acknowledgement = ack-nhfb,
}
@TechReport{Moses:1969:ICS,
author = "Joel Moses",
title = "The integration of a class of special functions with
the {Risch} algorithm",
type = "{AI} Memo (180)",
number = "MAC-M-421",
institution = "Artificial Intelligence Laboratory, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "13 + 1",
year = "1969",
LCCN = "Q334 M533 no. 180",
bibdate = "Sat Oct 30 18:37:28 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ng:1969:CPE,
author = "Edward W. Ng and C. J. Devine and R. F. Tooper",
title = "{Chebyshev} Polynomial Expansion of {Bose--Einstein}
Functions of Orders $1$ to $10$",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "639--643",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: $B_p(\eta) = \frac{1}{\Gamma(p - 1)}
\int_0^\infty \frac{x^p}{e^{x - \eta} - 1} \, dt$.
Relative errors down to $3 \times 10^{-19}$.",
}
@Article{Reichel:1969:IPV,
author = "Alex Reichel",
title = "The Integral of the $n$th Power of the {Voigt}
Function",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "645--649",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The function $\chi_n(t) =
\int_{-\infty}^\infty \{ U_0(x, t) \}^n \, dx$, where
$U_0(x, t) = \frac{1}{\sqrt{4 \pi t}} \frac{\exp[-(x -
y)^2 / 4 t]}{1 + y^2} \, dy$ is considered.",
}
@Article{Robertson:1969:CNC,
author = "G. H. Robertson",
title = "Computation of the Noncentral Chi-Square
Distribution",
journal = j-BELL-SYST-TECH-J,
volume = "48",
number = "1",
pages = "201--207",
month = jan,
year = "1969",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Sollfrey:1969:IFP,
author = "William Sollfrey",
title = "Inverse Functions of the Products of Two {Bessel}
Functions",
journal = j-J-MATH-PHYS,
volume = "10",
number = "8",
pages = "1429--1430",
month = aug,
year = "1969",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1664985",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:26 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "RAND Corp., Santa Monica, CA, USA",
keywords = "functions",
onlinedate = "4 November 2003",
pagecount = "2",
}
@Article{TadeudeMedeiros:1969:APF,
author = "Adilson {Tadeu de Medeiros} and Georges Schwachheim",
title = "{Algorithm 349}: {Polygamma} Functions with Arbitrary
Precision [{S14}]",
journal = j-CACM,
volume = "12",
number = "4",
pages = "213--214",
month = apr,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:25 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Lewis:1975:CPF}.",
abstract = "This procedure assigns to polygam the value of the
polygamma function of order n for any real argument
$z$. For $n = 0$, we have the psi or digamma function,
for $n = 1$ the trigamma function, for $n = 2$ the
tetragamma function, and so on.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7300 (Natural sciences computing)",
corpsource = "Centro Brasileiro de Pesquisas Fisicas, Rio de
Janeiro, Brazil",
keywords = "digamma function; mathematics; polygamma function; psi
function; special functions; subroutines; tetragamma
function; trigamma function",
remark = "Fullerton: 150-line Algol procedure.",
}
@InProceedings{Tesler:1969:AEF,
author = "G. S. Tesler",
booktitle = "Mathematical provisioning of electronic digital
computers and effective organization of the computing
process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
title = "The approximation of elementary functions by means of
polynomials of degree zero and one. ({Russian})",
publisher = "Akad. Nauk Ukrain. SSR",
address = "Kiev, USSR",
pages = "75--88",
year = "1969",
MRclass = "65D15",
MRnumber = "45 \#4600",
MRreviewer = "I. Selihova",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Turner:1969:DSC,
author = "L. R. Turner",
title = "Difficulty in {$\sin$\slash$\cos$} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{VandeVel:1969:SEM,
author = "H. {Van de Vel}",
title = "On the Series Expansion Method for Computing
Incomplete Elliptic Integrals of the First and Second
Kinds",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "61--69",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Zaker:1969:CCE,
author = "T. A. Zaker",
title = "Calculation of the complementary error function of
complex argument",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "3",
pages = "427--430",
month = oct,
year = "1969",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(69)90011-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Thu Dec 04 16:20:39 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
acknowledgement = ack-nhfb,
}
@Article{Bray:1970:CAR,
author = "T. Bray",
title = "Certification of {Algorithm 22, Ricatti--Bessel
Functions of First and Second Kind}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--448",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Oct 29 21:49:15 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: An error in an Algol procedure is
reported.",
}
@Article{Carlitz:1970:SRF,
author = "L. Carlitz",
title = "Some Reduction Formulas for Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "2",
pages = "243--245",
month = may,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:58 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Chen:1970:CGI,
author = "Reuven Chen",
title = "On the Computation of the Generalized Integral in Glow
Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "2",
pages = "314--316",
month = oct,
year = "1970",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(70)90027-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Fri Oct 29 22:09:19 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
}
@Article{Cochran:1970:NTF,
author = "James Alan Cochran and Judith N. Hoffspiegel",
title = "Numerical Techniques for Finding $\nu$-Zeros of
{Hankel} Functions",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "413--422",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Cody:1970:CAC,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the {Coulomb} Phase
Shift",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "671--677",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65.25",
MRnumber = "42\#8661",
bibdate = "Wed Jan 17 08:57:04 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Relative errors down to $4 \times
10^{-19}$.",
}
@Article{Cody:1970:RAC,
author = "W. J. Cody and Kathleen A. Paciorek",
title = "Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb}
Wave Functions",
journal = j-CACM,
volume = "13",
number = "9",
pages = "573",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Wed Nov 16 23:58:51 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: More modifications to an Algol procedure.",
}
@Article{Darlington:1970:AAA,
author = "Sidney Darlington",
title = "Analytical Approximations to Approximations in the
{Chebyshev} Sense",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "1",
pages = "1--32",
month = jan,
year = "1970",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@TechReport{DeLugish:1970:CAA,
author = "Bruce Gene DeLugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Functions in a Binary Computer",
number = "399",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "191",
year = "1970",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1970:RAD,
author = "Walter Gautschi and Bruce J. Klein",
title = "Remark on {Algorithm 282, Derivatives of $e^x / x$,
$\cos(x) / x$, and $\sin(x) / x$}",
journal = j-CACM,
volume = "13",
number = "1",
pages = "53--54",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sat Oct 30 07:27:17 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1966:AD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Corrections are given for several Algol
procedures.",
}
@Article{Gautschi:1970:RCC,
author = "Walter Gautschi and Bruce J. Klein",
title = "Recursive computation of certain derivatives --- {A}
study of error propagation",
journal = j-CACM,
volume = "13",
number = "1",
pages = "7--9",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "65Q05",
MRnumber = "46 1115",
MRreviewer = "D. F. Mayers",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A brief study is made of the propagation of errors in
linear first-order difference equations. The recursive
computation of successive derivatives of $(e^x)/x$ and
$(\cos x)/x$ is considered as an illustration.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
keywords = "difference equations; error analysis; error
propagation; recursive computation; successive
derivatives",
remark = "Fullerton: Recursive calculation of derivatives of
$e^x / x$ and $\cos(x) / x$ is considered.",
}
@Article{Hill:1970:AASa,
author = "G. W. Hill",
title = "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
journal = j-CACM,
volume = "13",
number = "10",
pages = "617--619",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
keywords = "statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Hill:1970:AASb,
author = "G. W. Hill",
title = "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
journal = j-CACM,
volume = "13",
number = "10",
pages = "619--620",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also
\cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
keywords = "function evaluation; statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Holmgren:1970:RAN,
author = "Bo Holmgren",
title = "Remark on {Algorithm 304, Normal Curve Integral}",
journal = j-CACM,
volume = "13",
number = "10",
pages = "624--624",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sat Oct 30 08:18:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Jones:1970:GHF,
author = "Alan L. Jones",
title = "The generalized hypergeometric function",
journal = j-SIGPLAN,
volume = "5",
number = "3",
pages = "26--27",
month = mar,
year = "1970",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:40:57 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kolbig:1970:CZI,
author = "K. S. Kolbig",
title = "Complex Zeros of an Incomplete {Riemann} Zeta Function
and of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "679--696",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@TechReport{Lugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "????",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Luke:1970:FAE,
author = "Yudell L. Luke",
title = "Further Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "191--198",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Minton:1970:GHF,
author = "Barry M. Minton",
title = "Generalized Hypergeometric Function of Unit Argument",
journal = j-J-MATH-PHYS,
volume = "11",
number = "4",
pages = "1375--1376",
month = apr,
year = "1970",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1665270",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:39:25 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "Univ. Calgary, Alta., Canada",
keywords = "functions",
onlinedate = "28 October 2003",
pagecount = "2",
}
@Article{Ng:1970:CAE,
author = "E. N. Ng",
title = "Certification of {Algorithm 385, Exponential Integral
{$\operatorname{Ei}(x)$}}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--449",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sat Oct 30 09:18:14 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Comments on a FORTRAN routine.",
}
@Article{Ng:1970:CDF,
author = "E. W. Ng and C. J. Devine",
title = "On the Computation of {Debye} Functions of Integer
Orders",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "405--407",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Debye functions are incomplete Riemann zeta
functions. $\overbar{D}_p(x) = \frac{1}{\Gamma(p - 1)}
\int_0^x \frac{t^p}{e^t - 1} \, dt$ and the
complementary integral are calculated to 20 digits.",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR
database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya Univ., Chikua ku, Japan",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Paciorek:1970:AEI,
author = "K. A. Paciorek",
title = "{Algorithm 385}: {Exponential} Integral
{$\operatorname{Ei}(x)$}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "446--447",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation);
C7300 (Natural sciences computing)",
corpsource = "Argonne Nat. Lab., IL, USA",
keywords = "integration; subroutines",
remark = "Fullerton: A 100-line FORTRAN routine for both
$\operatorname{E1}(x)$ and $\operatorname{Ei}(x)$.",
}
@Article{Raff:1970:CGF,
author = "Morton S. Raff",
title = "On Calculating the Gamma Function of Non-Integral
Arguments",
journal = j-AMER-STAT,
volume = "24",
number = "2",
pages = "22--24",
month = apr,
year = "1970",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 10:52:18 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326364;
http://www.math.utah.edu/pub/tex/bib/amstat1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2681926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@Article{Redish:1970:RAE,
author = "K. A. Redish",
title = "Remark on {Algorithm 385, Exponential Integral
$\operatorname{Ei}(x)$}",
journal = j-CACM,
volume = "13",
number = "12",
pages = "750--750",
month = dec,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sat Oct 30 09:56:59 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Paciorek:1970:AEI}",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Minor corrections to a FORTRAN routine.",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems {Hydra X8}} \toenglish {Documentation}
of the Elementary Functions of the Operating System
{Hydra X8} \endtoenglish",
type = "Interner {Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1970",
bibdate = "Fri Jun 11 12:37:53 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Smith:1970:ASH,
author = "Robert R. Smith and Dennis McCall",
title = "{Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}",
journal = j-CACM,
volume = "13",
number = "9",
pages = "567--570",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
classcodes = "C4170 (Differential equations); C7310 (Mathematics
computing)",
corpsource = "US Naval Electronics Lab. Center, San Diego, CA, USA",
keywords = "boundary-value problems; partial differential
equations",
}
@Article{Squire:1970:RAI,
author = "William Squire",
title = "A Rational Approximation to an Integral Appearing in
Glow Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "1",
pages = "152--253",
month = aug,
year = "1970",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(70)90016-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 10:57:00 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
}
@Article{Srivastava:1970:CRI,
author = "H. M. Srivastava",
title = "Certain Results Involving Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "1",
pages = "75--81",
month = feb,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:56 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Stegun:1970:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
Part 1. {Error}, Probability, and Related Functions",
journal = "J. Res. Nat. Bur. Stand.",
volume = "74B",
number = "3",
pages = "211--224",
month = jul,
year = "1970",
bibdate = "Sat Oct 30 10:58:39 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $\erf$ and $\erfc$.",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Tue Apr 08 20:38:30 1997",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@TechReport{Yohe:1970:RBC,
author = "J. M. Yohe",
title = "Rigorous Bounds on Computed Approximations to Square
Roots and Cube Roots",
type = "MRC Technical Summary",
number = "1088",
institution = "University of Wisconsin, Madison",
year = "1970",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr,
}
@Article{Zill:1970:SEI,
author = "D. G. Zill and B. C. Carlson",
title = "Symmetric Elliptic Integrals of the Third Kind",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "199--214",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Bohan:1971:ADC,
author = "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
title = "The analytic definition of certain elementary
functions. ({Russian}) Questions of modern mathematics
and methods of teaching it at institutions of higher
learning",
journal = "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
volume = "404",
pages = "59--78",
year = "1971",
MRclass = "26A09",
MRnumber = "55 \#10612",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $x(1\pm2^{-m})$
can be evaluated by a shift followed by an add. A pair
of numbers $(x_k, y_k)$ can represent a function $x:
f(x)= g(x_k, y_k)$, such that $g(l,y_n) = y_n$ for
logarithm, quotient and square root. Then,
multiplication by shifting is applied to $x_k$ with
suitable adjustments on $y_k$, until $x_k$ is close to
unity, at which time $y_k$ represents the desired
answer. The exponential is computed by essentially
reversing the logarithm procedure. A termination
algorithm further improves accuracy. The apparatus
involves two registers for $x_k$ and $y_k$, a local
memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Cody:1971:CAR,
author = "W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher,
Jr.}",
title = "{Chebyshev} approximations for the {Riemann} zeta
function",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "537--547",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20",
MRnumber = "47 2785",
bibdate = "Wed Jan 17 08:57:00 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 20-digit approximations for either
$\zeta(s)$ or $\zeta(s) - 1$.",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Glasser:1971:CFE,
author = "M. L. Glasser and V. E. Wood",
title = "A Closed Form Evaluation of the Elliptic Integral",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "535--536",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Glasser:1971:EII,
author = "M. L. Glasser",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "533--534",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Herman:1971:EDH,
author = "G. T. Herman",
title = "The equivalence of different hierarchies of elementary
functions",
journal = "Z. Math. Logik Grundlagen Math.",
volume = "17",
pages = "219--224",
year = "1971",
MRclass = "02.77 (68.00)",
MRnumber = "44 \#6494",
MRreviewer = "D. A. Clarke",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compj.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries{}\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Liron:1971:ISR,
author = "N. Liron",
title = "Infinite Sums of Roots for a Class of Transcendental
Equations and {Bessel} Functions of Order One-Half",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "769--781",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Lucas:1971:AAC,
author = "C. W. {Lucas, Jr.} and C. W. Terrill",
title = "{ACM Algorithm 404}: Complex Gamma Function [{S14}]",
journal = j-CACM,
volume = "14",
number = "1",
pages = "48--49",
month = jan,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 07:00:03 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "Coll. William and Mary, Williamsburg, VA, USA",
keywords = "algorithm; CGAMMA; complex gamma function evaluation;
formula; function evaluation; poles of gamma function;
recursion formula; reflection; Stirling's asymptotic
series; subroutine in ALGOL; subroutines",
oldlabel = "LucasT71",
remark = "Fullerton: Fortran routine with machine-dependent
constants.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/LucasT71",
}
@Article{Luke:1971:MTBa,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "323--330",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Luke:1971:MTBb,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions, {II}",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "789--795",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Matta:1971:UCE,
author = "F. Matta and A. Reichel",
title = "Uniform Computation of the Error Function and Other
Related Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "339--344",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 01 10:32:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@Article{Scarton:1971:DPF,
author = "Henry A. Scarton",
title = "Double precision {FORTRAN} subroutines to compute both
ordinary and modified {Bessel} functions of the first
kind and of integer order with arbitrary complex
argument: {$J_n(x + j y)$} and {$I_n(x + j y)$}",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "2",
pages = "295--299",
month = oct,
year = "1971",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(71)90010-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fortran1.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999171900106",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
}
@Article{Shenton:1971:CFP,
author = "L. R. Shenton and K. O. Bowman",
title = "Continued Fractions for the Psi Function and its
Derivatives",
journal = j-SIAM-J-APPL-MATH,
volume = "20",
number = "4",
pages = "547--554",
month = jun,
year = "1971",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2099856",
acknowledgement = ack-nhfb,
}
@Article{Shipman:1971:HSE,
author = "L. L. Shipman and R. E. Christoffersen",
title = "High Speed Evaluation of {$F_0(x)$}",
journal = j-COMP-PHYS-COMM,
volume = "2",
number = "4",
pages = "201--206",
month = may # "\slash " # jun,
year = "1971",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(71)90053-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:40:08 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465571900531",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
remark = "Fullerton: $F_0(x) = \int_0^1 \exp(-x u^2) \, du$,
which is simply related to $\erf$ for $x > 0$ and to
Dawson's function for $x < 0$.",
}
@Article{Spellucci:1971:DPA,
author = "P. Spellucci",
title = "Double precision approximations to the elementary
functions using {Jacobi-fractions}",
journal = j-NUM-MATH,
volume = "18",
pages = "127--143",
year = "1971/1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
MRclass = "65D20",
MRnumber = "45 \#7938",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Spira:1971:CGF,
author = "Robert Spira",
title = "Calculation of the Gamma Function by {Stirling}'s
Formula",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "317--322",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Sundblad:1971:AFT,
author = "Y. Sundblad",
title = "The {Ackermann} Function. {A} Theoretical,
Computational, and Formula Manipulative Study",
journal = j-BIT,
volume = "11",
number = "1",
pages = "107--119",
month = mar,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01935330",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:11 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Ackermann's function is a recursively
defined function of importance to computer science
theorists.",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Wills:1971:URR,
author = "John G. Wills",
title = "On the use of recursion relations in the numerical
evaluation of spherical {Bessel} functions and
{Coulomb} functions",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "1",
pages = "162--166",
month = aug,
year = "1971",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(71)90043-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199917190043X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Wong:1971:SEI,
author = "R. Wong and E. Rosenbloom",
title = "Series Expansions of ${W}_{k,m}(z)$ Involving
Parabolic Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "783--787",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bardin:1972:CFE,
author = "C. Bardin and Y. Dandeu and L. Gauthier and J.
Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and
T. Tamura",
title = "{Coulomb} Functions in Entire $(\eta, \rho)$ Plane",
journal = j-COMP-PHYS-COMM,
volume = "3",
number = "2",
pages = "73--87",
month = mar,
year = "1972",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(72)90057-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:09:33 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Book{Bark:1972:MTF,
author = "L. S. Bark",
title = "{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
funktsi{\u{\i}}} ($\operatorname{sin} x$,
$\operatorname{cos} x$, $e^{x}$ {\cyr i} $e^{-x}$).
({Russian}) [Multiplace tables of the elementary
functions ($\operatorname{sin}\ x$,
$\operatorname{cos}\ x$, $e^{x}$ and $e^{-x}$)]",
publisher = "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
address = "Moscow, USSR",
edition = "Second, unrevised",
pages = "134",
year = "1972",
MRclass = "65A05",
MRnumber = "50 \#6100",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Tables processed and text translated from the English
by L. S. Bark. Library of Mathematical Tables, No. 9.
1972",
acknowledgement = ack-nhfb,
}
@Article{Carlson:1972:ACL,
author = "B. C. Carlson",
title = "An algorithm for computing logarithms and
arctangents",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "543--549",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Iowa State Univ., Ames, IA, USA",
keywords = "acceleration; arctangents; auxiliary; Borchardt's
algorithm; convergence; fast; function approximation;
functions; inverse circular functions; inverse
hyperbolic; iterative algorithm; logarithms; numerical
methods; rational operations; recurrence relation;
square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $(x, y)$ such that the $F(x, y) = f(x_0)$ is
invariant; when $x$ is driven towards a known value
$x_w$, $y$ is driven towards the result. For an $N$-bit
fraction about $N / 4$ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@TechReport{Ercegovac:1972:RES,
author = "Milos D. Ercegovac",
title = "Radix 16 Evaluation of Some Elementary Functions",
number = "540",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "30",
year = "1972",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Frisch:1972:RAR,
author = "Michael J. Frisch",
title = "Remark on ``{Algorithms 352, 385, 392}: Remarks on
Characteristic Values and Associated Solutions of
{Mathieu}'s Differential Equation, Exponential
Integral, and Systems of Hyperbolic {P.D.E.}''",
journal = j-CACM,
volume = "15",
number = "12",
pages = "1074--??",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:42:24 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.",
acknowledgement = ack-nhfb,
oldlabel = "Frisch72",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Frisch72",
}
@Article{Fullerton:1972:MIG,
author = "W. Fullerton",
title = "{ACM Algorithm 435}: Modified Incomplete Gamma
Function",
journal = j-CACM,
volume = "15",
number = "11",
pages = "993--995",
month = nov,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 09:47:55 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Schoene:1978:RMI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Fortran subprogram for evaluating $e^{x_1}
\int_{x_1}^{x_2} |y|^{a - 1} e^{-y} \, dy$ for $a$
roughly between $1$ and $2$.",
}
@Article{Hunter:1972:NEC,
author = "D. B. Hunter and T. Regan",
title = "A note on the evaluation of the complementary error
function",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "539--541",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Bradford, UK",
keywords = "complementary error function; complex variable;
evaluation; integration; method of Matta and Reichel;
modification; numerical; stability",
treatment = "T Theoretical or Mathematical",
}
@Article{Kim:1972:AEH,
author = "Shoon K. Kim",
title = "The Asymptotic Expansion of a Hypergeometric Function
$_2{F}_2(1, \alpha; \rho_1, \rho_2; z)$",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "963--963",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Kolbig:1972:CAC,
author = "K. S. K{\"o}lbig",
title = "Certification of ``{Algorithm 363}: {Complex} error
function''",
journal = j-CACM,
volume = "15",
number = "6",
pages = "465--466",
month = jun,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:55:38 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1969:ACE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CERN, Geneva, Switzerland",
keywords = "$\erf(z)$; complex error function; function
evaluation; special functions; subroutines; Voigt
function",
oldlabel = "Kolbig72",
remark = "Fullerton: Corrections and tests of an Algol
procedure.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kolbig72",
}
@Article{Kolbig:1972:PCL,
author = "K. S. K{\"o}lbig",
title = "Programs for Computing the Logarithm of the Gamma
Function, and the Digamma Function, for Complex
Argument",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "221--226",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(72)90012-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:33:42 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Kolbig:1972:RCC,
author = "K. S. K{\"o}lbig",
title = "Remarks on the Computation of {Coulomb}
Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "214--220",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(72)90011-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:35:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Kolbig:1972:ZIG,
author = "K. S. Kolbig",
title = "On the Zeros of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "26",
number = "119",
pages = "751--755",
month = jul,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "CERN, Geneva, Switzerland",
keywords = "asymptotic formulae; complex w plane; function
approximation; incomplete gamma function; poles and
zeros; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Kuki:1972:AAC,
author = "Hirondo Kuki",
title = "{ACM Algorithm 421}: Complex Gamma Function with Error
Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "271--272",
month = apr,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: 100-line FORTRAN routine with double
complex accuracy to $10^{-14}$.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Article{Kuki:1972:CGF,
author = "Hirondo Kuki",
title = "Complex Gamma Function with Error Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "262--267",
month = apr,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: Description of a FORTRAN routine with some
math details.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Book{Lebedev:1972:SFT,
author = "N. N. (Nikolai Nikolaevich) Lebedev",
title = "Special functions and their applications",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xii + 308",
year = "1972",
ISBN = "0-486-60624-4 (paperback)",
ISBN-13 = "978-0-486-60624-8 (paperback)",
LCCN = "QA351 .L3613 1972",
bibdate = "Sat Oct 30 16:25:05 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated to English and edited by Richard A.
Silverman.",
URL = "http://www.loc.gov/catdir/description/dover031/72086228.html",
acknowledgement = ack-nhfb,
remark = "Translation of Spe{\"e}t{\`\i}sial\S{}nye
funk{\"e}t{\`\i}sii i ikh prilozheni{\"e}i{\`\i}a.",
subject = "Functions, Special; Mathematical physics",
}
@Article{Ling:1972:EM,
author = "Chih-Bing Ling and Jung Lin",
title = "On Evaluation of Moments of ${K}_\nu(t)/{I}_\nu(t)$",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "529--537",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Virginia Politech. Inst., Blacksburg, VA, USA",
keywords = "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
numerical methods; Watson's method",
treatment = "T Theoretical or Mathematical",
}
@Article{Linz:1972:MCB,
author = "Peter Linz",
title = "A Method for Computing {Bessel} Function Integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "509--513",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davis, CA, USA",
keywords = "Abel; Bessel function integrals; Fourier integrals;
infinite integrals; integration; numerical computation;
transform",
treatment = "T Theoretical or Mathematical",
}
@Article{Luke:1972:MTB,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions. {III}",
journal = j-MATH-COMPUT,
volume = "26",
number = "117",
pages = "237--240",
month = jan,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Univ. Missouri, Kansas City, KS, USA",
keywords = "Bessel functions; miniaturized tables; numerical
methods",
treatment = "T Theoretical or Mathematical",
}
@Article{MacKinnon:1972:AEH,
author = "Robert F. MacKinnon",
title = "The asymptotic expansions of {Hankel} transforms and
related integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "515--527",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Defence Res. Establ., Pacific, Victoria, BC, Canada",
keywords = "asymptotic expansions; Bessel; functions; Hankel
transforms; integrals; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = "NASA",
address = "Washington, DC, USA",
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Morita:1972:CAG,
author = "Tohru Morita and Tsuyoshi Horiguchi",
title = "Convergence of the arithmetic-geometric mean procedure
for the complex variables and the calculation of the
complete elliptic integrals with complex modulus",
journal = j-NUM-MATH,
volume = "20",
number = "5",
pages = "425--430",
month = oct,
year = "1972",
CODEN = "NUMMA7",
DOI = "http://dx.doi.org/10.1007/BF01402565",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Jan 13 10:01:46 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
abstract = "The convergence of the arithmetic-geometric mean
procedure is checked for complex variables. The
procedure is shown to be useful for the evaluation of
the complete elliptic integrals of the first and second
kinds with complex modulus. It is suggested that the
procedure will be useful also for the numerical
calculation of the elliptic integrals and the Jacobian
elliptic functions with complex modulus in general.",
acknowledgement = ack-nhfb,
}
@Article{Moses:1972:TGT,
author = "Joel Moses",
title = "Toward a General Theory of Special Functions",
journal = j-CACM,
volume = "15",
number = "7",
pages = "550--554",
month = jul,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "34-02 12H05",
MRnumber = "53 3384",
MRreviewer = "K. Okugawa",
bibdate = "Mon Jan 22 07:06:21 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/macsyma.bib",
note = "Twenty-fifth anniversary of the Association for
Computing Machinery.",
acknowledgement = ack-nhfb,
classcodes = "C1100 (Mathematical techniques)",
keywords = "general theory; mathematics; special functions",
oldlabel = "Moses72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Moses72",
}
@Article{Olver:1972:NBR,
author = "F. W. J. Olver and D. J. Sookne",
title = "Note on Backward Recurrence Algorithms",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "941--947",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290Z (Other numerical methods); C4190 (Other
numerical methods)",
corpsource = "Univ. Maryland, College Park, MD, USA",
keywords = "backward recurrence algorithms; Bessel; Bessel
functions; difference equations; functions; recessive
solution; second order linear difference equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Parnes:1972:CZM,
author = "R. Parnes",
title = "Complex zeros of the modified {Bessel} function
{$K_n(Z)$}",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "949--953",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "City Univ., New York, NY, USA",
keywords = "and zeros; Bessel functions; complex zeros;
interpolation; interpolation scheme; iterative;
iterative methods; modified Bessel function; poles",
treatment = "T Theoretical or Mathematical",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Samet:1972:CDS,
author = "P. A. Samet",
title = "Calculation of a double-length square root from
double-length number using single precision
techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Mon Jul 26 14:05:09 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compj.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Strecok:1972:HPE,
author = "A. J. Strecok and J. A. Gregory",
title = "High Precision Evaluation of the Irregular {Coulomb}
Wave Functions",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "955--961 + s1--s10",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "A0365G (Solutions of wave equations: bound state in
quantum theory); B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
keywords = "function approximation; high precision evaluation;
irregular Coulomb wave functions; numerical methods;
wave functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Turunov:1972:EFD,
author = "M. Turunov",
title = "Elementary functions of a discrete real and complex
argument. ({Russian})",
journal = "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
volume = "418 Voprosy Mat.",
pages = "263--271, 386",
year = "1972",
MRclass = "30A95",
MRnumber = "50 \#13556",
MRreviewer = "G. Berzsenyi",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Wynn:1972:CAM,
author = "P. Wynn",
title = "Convergence Acceleration by a Method of
Intercalation",
journal = j-COMPUTING,
volume = "9",
number = "4",
pages = "267--273",
year = "1972",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Louisiana State Univ., New Orleans, LA, USA",
classification = "B0290Z; C4190",
description = "convergence; series (mathematics)",
keywords = "convergence acceleration; method of intercalation;
series of real terms",
}
@Article{Amos:1973:BIC,
author = "D. E. Amos",
title = "Bounds on Iterated Coerror Functions and Their
Ratios",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "413--427",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Baker:1973:PAS,
author = "P. W. Baker",
title = "Predictive algorithms for some elementary functions in
radix $2$",
journal = j-ELECT-LETTERS,
volume = "9",
pages = "493--494",
year = "1973",
CODEN = "ELLEAK",
ISBN = "0013-5194",
ISBN-13 = "0013-5194",
ISSN = "0013-5194",
MRclass = "68A10",
MRnumber = "57 \#18203",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Braithwaite:1973:ALP,
author = "W. J. Braithwaite",
title = "Associated {Legendre} Polynomials, Ordinary and
Modified Spherical Harmonics",
journal = j-COMP-PHYS-COMM,
volume = "5",
number = "5",
pages = "390--394",
month = may,
year = "1973",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(73)90065-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:45:41 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Cody:1973:CAP,
author = "W. J. Cody and Anthony J. Strecok and Henry C.
{Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Psi Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "123--127",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65-06 (68-06)",
MRnumber = "50 6095",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
keywords = "Chebyshev approximation; Chebyshev approximations;
digamma function; psi function",
remark = "Fullerton: Relative errors down to $10^{-20}$",
treatment = "T Theoretical or Mathematical",
}
@Article{Ercegovac:1973:REC,
author = "M. D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Fettis:1973:CZE,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Complex zeros of the error function and of the
complementary error function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "401--407",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
keywords = "asymptotic formula; complementary error function;
complex zeros; error function; errors; first one
hundred zeros; function evaluation; poles and zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Fettis:1973:SPC,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Saddle Points of the Complementary Error Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "409--412",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
keywords = "asymptotic; complementary error function; errors;
formula; function evaluation; poles and zeros; saddle
points",
treatment = "T Theoretical or Mathematical",
}
@Article{Gautschi:1973:AAE,
author = "Walter Gautschi",
title = "{ACM Algorithm 471}: Exponential Integrals [{S13}]",
journal = j-CACM,
volume = "16",
number = "12",
pages = "761--763",
month = dec,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:43:23 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation);
C7310 (Mathematics computing)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
keywords = "ALGOL; computation; continued fractions; exponential
integrals; integration; recurrence relations;
recursive; subroutine; subroutines",
oldlabel = "Gautschi73",
remark = "Fullerton: Algol-language routine for $E_n(x) =
\int_1^\infty e^{-x t} t^n \, dt, x > 0$.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gautschi73",
}
@TechReport{Hemker:1973:SDL,
author = "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
and H. L. Oudshoorn and D. T. Winter",
title = "Single- and double-length computation of elementary
functions",
number = "NW 7",
institution = "Mathematical Centre",
address = "Amsterdam",
year = "1973",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1973:AAN,
author = "G. W. Hill and A. W. Davis",
title = "{ACM Algorithm 442}: Normal Deviate [{S14}]",
journal = j-CACM,
volume = "16",
number = "1",
pages = "51--52",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:49:54 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
country = "USA",
descriptors = "RVG;",
enum = "7393",
keywords = "ALGOL; normal deviate; normal distribution inverse;
probit; statistics; subroutines; Taylor series
approximation; transform",
language = "English",
oldlabel = "HillD73",
references = "0",
remark = "Fullerton: Short Algol-language procedure with
accuracy to 24 digits.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HillD73",
}
@Article{Hill:1973:AAS,
author = "G. W. Hill",
title = "{ACM Algorithm 465}: {Student}'s $t$ Frequency
[{S14}]",
journal = j-CACM,
volume = "16",
number = "11",
pages = "690--690",
month = nov,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:49:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, SA, Australia",
keywords = "ALGOL; approximation; density function; series;
statistics; student's t statistic; subroutine;
subroutines",
oldlabel = "Hill73a",
remark = "Fullerton: Algol-language routine for $f(t | n) =
\frac{\Gamma(n/2 + 1/2)}{(\pi n)^{1/2} \Gamma(n/2)} (1
+ t^2 / n)^{n/2 + 1/2}$.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hill73a",
}
@Article{Laurenzi:1973:DWF,
author = "Bernard J. Laurenzi",
title = "Derivatives of {Whittaker} Functions ${W}_{k, 1/2}$
and ${M}_{k, 1/2}$ with Respect to Order ${K}$",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "129--132",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Levin:1973:DNL,
author = "D. Levin",
title = "Development of non-linear transformations for
improving convergence of sequences",
journal = j-INT-J-COMPUT-MATH,
volume = "3",
number = "1--4",
pages = "371--388",
month = "????",
year = "1973",
CODEN = "IJCMAT",
DOI = "http://dx.doi.org/10.1080/00207167308803075",
ISSN = "0020-7160",
ISSN-L = "0020-7160",
bibdate = "Thu Dec 01 10:27:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer Mathematics",
keywords = "convergence acceleration",
ZMnumber = "0274.65004",
}
@Article{Linz:1973:NCI,
author = "Peter Linz and T. E. Kropp",
title = "A note on the computation of integrals involving
products of trigonometric and {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "871--872",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davies, CA, USA",
keywords = "Bessel functions; computation; integration; numerical;
numerical methods; products; trigonometric",
treatment = "T Theoretical or Mathematical",
}
@Article{Lozier:1973:BCP,
author = "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
title = "A bit comparison program for algorithm testing",
journal = j-COMP-J,
volume = "16",
number = "2",
pages = "111--117",
month = may,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
acknowledgement = ack-nhfb,
classcodes = "C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Nat. Bur. Stand., Washington, DC, USA",
keywords = "accuracy; algorithm testing; bit comparison program;
computer algorithms; program debugging",
treatment = "P Practical",
}
@Article{McNolty:1973:SPD,
author = "Frank McNolty",
title = "Some probability density functions and their
characteristic functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "495--504",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0240 (Probability and statistics); C1140 (Probability
and statistics)",
corpsource = "Lockheed Palo Alto Res. Lab., CA, USA",
keywords = "Bessel function; characteristic functions; functions;
hypergeometric function; probability; probability
density functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Rice:1973:EEI,
author = "S. O. Rice",
title = "Efficient Evaluation of Integrals of Analytic
Functions by the Trapezoidal Rule",
journal = j-BELL-SYST-TECH-J,
volume = "52",
number = "5",
pages = "707--722",
month = may # "--" # jun,
year = "1973",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "decimal fixed-point arithmetic",
}
@Article{Sookne:1973:BFC,
author = "D. J. Sookne",
title = "{Bessel} Functions {$I$} and {$J$} of Complex Argument
and Integer Order",
journal = "J. Res. Nat. Bur. Stand.",
volume = "77B",
number = "3--4",
pages = "111--114",
month = jul,
year = "1973",
bibdate = "Sat Oct 30 10:49:13 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: A program is described but not published.",
}
@Article{Sookne:1973:BFR,
author = "D. J. Sookne",
title = "{Bessel} Functions of Real Argument and Integer
Order",
journal = "J. Res. Nat. Bur. Stand.",
volume = "77A",
number = "3--4",
pages = "125--132",
month = jul,
year = "1973",
bibdate = "Sat Oct 30 10:51:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Sequences of $I_n(x)$ and $J_n(x)$ are
computed with a FORTRAN routine.",
}
@Article{Sookne:1973:CABa,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Real Argument",
journal = "J. Res. Nat. Bur. Stand.",
volume = "77B",
number = "3--4",
pages = "115--124",
month = jul,
year = "1973",
bibdate = "Sat Oct 30 10:55:03 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: An algorithm is shown to lose at most about
3 bits of precision.",
}
@Article{Sookne:1973:CABb,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Complex Argument",
journal = "J. Res. Nat. Bur. Stand.",
volume = "77B",
number = "3",
pages = "133--136",
month = jul,
year = "1973",
bibdate = "Sat Oct 30 10:53:39 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The algorithm is shown to lose at most
about 3 bits of precision.",
}
@Article{Vos:1973:RAC,
author = "H. Vos",
title = "Remark on ``{Algorithm 300}: {Coulomb} Wave
Functions''",
journal = j-CACM,
volume = "16",
number = "5",
pages = "308--309",
month = may,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 07:27:34 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gunn:1967:ACW}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "Vrije Univ., Amsterdam, Netherlands",
keywords = "Coulomb wave functions; function evaluation;
mathematics; wave functions",
oldlabel = "Vos73",
remark = "Fullerton: Algol-language accuracy monitor for
Algorithm 300, which is generally accurate only to 3
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Vos73",
}
@Article{Wong:1973:AEL,
author = "R. Wong",
title = "An Asymptotic Expansion of {$W_{k,m}(z)$} with Large
Variable and Parameters",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "429--436",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Wrench:1973:ECT,
author = "John W. Wrench",
title = "Erratum: {Concerning Two Series for the Gamma
Function}",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "681--682",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Minor last-digit rounding errors are
reported.",
}
@Article{Wrigge:1973:EII,
author = "H. S. Wrigge",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "839--840",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
month = mar,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Acton:1974:RRF,
author = "Forman S. Acton",
title = "Recurrence relations for the {Fresnel} integral
$\int_0^{\infty} \exp(-ct) \, dt / \sqrt{t (1 + t^2)}$
and similar integrals",
journal = j-CACM,
volume = "17",
number = "8",
pages = "480--481",
month = aug,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20 (33A70)",
MRnumber = "49 6554",
bibdate = "Mon Jan 22 06:20:27 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The class of functions defined by
$\int_0^\infty[\exp(- cX)dt/(1+Y)(t^{1/2})^k]$ where
$X$ and $Y$ are either $t$ or $t^2$ and $k$ is $-1$,
$0$, or $1$ can be evaluated by recurrences for all but
small values of the parameter $c$. These recurrences,
given here, are more efficient than the usual
asymptotic series.",
acknowledgement = ack-nhfb,
classification = "921",
journalabr = "Commun ACM",
keywords = "exponential integral; Fresnel integral; mathematical
techniques; recurrence relations",
oldlabel = "Acton74",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Acton74",
}
@Article{Amos:1974:CMB,
author = "D. E. Amos",
title = "Computation of modified {Bessel} functions and their
ratios",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "239--251",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
keywords = "Bessel functions; computation; low order Bessel
functions; modified Bessel functions; monotonicity;
properties; ratios; recursion; relation",
remark = "Fullerton: Ratios $I_{\nu + 1}(x) / I_\nu(x)$ are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Article{Barlow:1974:CCF,
author = "R. H. Barlow",
title = "Convergent Continued Fraction Approximant's to
Generalised Polylogarithms",
journal = j-BIT,
volume = "14",
number = "1",
pages = "112--116",
month = mar,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933124",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:13 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Nielsen's generalization $S_{n, p}(z) =
\frac{(-1)^{n + p - 1}}{(n - 1)! p!} \int_0^1 \ln^{n -
1}(t) \ln^p(1 - zt) / t \, dt$ is evaluated in the
complex plane.",
}
@Article{Barnett:1974:CWF,
author = "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
B. Goldfarb",
title = "{Coulomb} wave functions for all real $\eta$ and
$\rho$",
journal = j-COMP-PHYS-COMM,
volume = "8",
number = "5",
pages = "377--395",
month = dec,
year = "1974",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(74)90013-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Jul 14 09:47:42 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "This paper may contain the first presentation of
Steed's algorithm for computing continued fractions.",
}
@Article{Blair:1974:RCA,
author = "J. M. Blair",
title = "Rational {Chebyshev} approximations for the modified
{Bessel} functions {$I_0(x)$} and {$I_1(x)$}",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "581--583",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
keywords = "Chebyshev approximation; functions; modified Bessel;
nearly best rational approximations; rational Chebyshev
approximations; series (mathematics)",
remark = "Fullerton: With microfiche supplement. Relative errors
down to $10^{-23}$.",
treatment = "T Theoretical or Mathematical",
}
@Article{Bosten:1974:RAI,
author = "Nancy E. Bosten and E. L. Battiste",
title = "Remark on ``{Algorithm 179}: {Incomplete} Beta
Ratio''",
journal = j-CACM,
volume = "17",
number = "3",
pages = "156--157",
month = mar,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:27:36 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.",
acknowledgement = ack-nhfb,
bdate = "Mon Jan 22 06:27:36 MST 2001",
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
corpsource = "IMSL, Houston, TX, USA",
keywords = "Algorithm 179; computer aided analysis; function
approximation; incomplete beta ratio; subroutines",
oldlabel = "BostenB74",
remark = "Fullerton: FORTRAN routine with accuracy about
$10^{-6}$. See M. C. Pike (1976) for a Remark.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BostenB74",
}
@Article{Brent:1974:AAG,
author = "Richard P. Brent",
title = "{ACM Algorithm 488}: {A} {Gaussian} pseudo-random
number generator [{G5}]",
journal = j-CACM,
volume = "17",
number = "12",
pages = "704--706",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:28:05 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7890 (Other special applications of computing)",
corpsource = "Australian Nat. Univ., Canberra, Australia",
country = "USA",
descriptors = "RVG;",
enum = "7061",
keywords = "distribution; FORTRAN; Gaussian; generator; GRAND;
normal distribution; pseudo random numbers; random
number generation; random numbers; subroutines",
language = "English",
location = "SEL: Wi",
oldlabel = "Brent74",
references = "0",
remark = "Fullerton: A FORTRAN routine that returns normally
distributed numbers with zero mean and unit standard
deviation.",
revision = "16/01/94",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Brent74",
}
@Article{Burrell:1974:AAE,
author = "Keith H. Burrell",
title = "{ACM Algorithm 484}: Evaluation of the Modified
{Bessel} Functions {$K_0(z)$} and {$K_1(z)$} for
Complex Arguments [{S17}]",
journal = j-CACM,
volume = "17",
number = "9",
pages = "524--526",
month = sep,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:28:58 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "California Inst. Technol., Pasadena, CA, USA",
keywords = "algorithm; applications of computers; Bessel
functions; complex arguments; function evaluation;
Gauss-Hermite quadrature; Hankel functions; modified
Bessel functions; natural sciences; subroutines",
oldlabel = "Burrell74",
remark = "Fullerton: 10-digit accuracy FORTRAN program.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Burrell74",
}
@Article{Buschman:1974:FSR,
author = "R. G. Buschman",
title = "Finite sum representations for partial derivatives of
special functions with respect to parameters",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "817--824",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Wyoming, Laramie, WY, USA",
keywords = "Bessel functions; differentiation; finite sum
representations; finite sums; functions; G function;
Gegenbauer functions; hypergeometric; Legendre; Mellin
transformation; partial derivatives; special functions;
Whittaker functions",
remark = "Fullerton: Whittaker and Bessel functions are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $x_{n+1} = 0.5 (x_n
+ a / x_n)$ to $c_n$ where $c_n \rightarrow 0.5$,
thereby increasing the asymptotic rate of convergence
from $e_{n+1} = 0.5 e_n^2$ to $e_{n+1} = 0.25 e_n^2$.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
}
@Article{Fettis:1974:SAC,
author = "Henry E. Fettis",
title = "A stable algorithm for computing the inverse error
function in the `tail-end' region",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "585--587",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
keywords = "function evaluation; inverse error function; iterative
algorithm; stability; stable algorithm; tail end
region",
treatment = "T Theoretical or Mathematical",
}
@Article{Glasser:1974:SDI,
author = "M. L. Glasser",
title = "Some definite integrals of the product of two {Bessel}
functions of the second kind: (order zero)",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "613--615",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Battelle Memorial Inst., Columbus, OH, USA",
keywords = "Bessel functions; definite integrals; evaluate;
function evaluation; integral representation; order;
second kind; zero",
treatment = "T Theoretical or Mathematical",
}
@Article{Koppelaar:1974:CRA,
author = "Henk Koppelaar",
title = "Certification and Remark on ``{Algorithm 191}:
Hypergeometric''",
journal = j-CACM,
volume = "17",
number = "10",
pages = "589--590",
month = oct,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:55:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Relph:1963:AH}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Utrecht State Univ., Netherlands",
keywords = "algorithm; hypergeometric; improvements; inefficiency;
natural sciences applications of computers;
subroutines",
oldlabel = "Kopelaar74",
remark = "Fullerton: Algol-language modifications for Algorithm
191, which does not appear to be accurate far from the
origin.",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kopelaar74",
}
@Article{Kyriakopoulos:1974:GFH,
author = "E. Kyriakopoulos",
title = "Generating functions of the hypergeometric functions",
journal = j-J-MATH-PHYS,
volume = "15",
number = "6",
pages = "753--759",
month = jun,
year = "1974",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.1666724",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:40:13 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1",
acknowledgement = ack-nhfb,
classification = "A0210 (Algebra, set theory, and graph theory); A0220
(Group theory); A0230 (Function theory, analysis)",
corpsource = "Nuclear Res. Center 'Democritos', Athens, Greece",
keywords = "functions; generating functions; hypergeometric
functions; Lie groups; Lie theory; multiplier
representation theory; Weisner's technique",
onlinedate = "4 November 2003",
pagecount = "7",
treatment = "T Theoretical or Mathematical",
}
@Article{Latham:1974:CPC,
author = "W. P. Latham and Rogers W. Redding",
title = "On the calculation of the parabolic cylinder
functions",
journal = j-J-COMPUT-PHYS,
volume = "16",
number = "1",
pages = "66--75",
month = sep,
year = "1974",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(74)90104-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:15 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999174901041",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{McCabe:1974:CFE,
author = "J. H. McCabe",
title = "A continued fraction expansion, with a truncation
error estimate, for {Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "811--816",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Univ. St. Andrews, Fife, UK",
keywords = "continued fraction expansion; convergents; Dawson's
integral; error analysis; function approximation;
rational approximations; truncation error estimate",
treatment = "T Theoretical or Mathematical",
}
@Article{Nasell:1974:IMB,
author = "Ingemar Nasell",
title = "Inequalities for Modified {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "253--256",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Bell Labs., Holmdel, NJ, USA",
keywords = "Bessel functions; inequalities; modified Bessel
functions; sharp versions",
treatment = "T Theoretical or Mathematical",
}
@Book{Olver:1974:ASF,
author = "F. W. J. Olver",
title = "Asymptotics and Special Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvi + 572",
year = "1974",
ISBN = "0-12-525850-X",
ISBN-13 = "978-0-12-525850-0",
LCCN = "QA351 .O481 1974",
bibdate = "Wed Dec 15 10:40:06 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pisarskii:1974:QCD,
author = "A. V. Pisarski{{\u{\i}}} and A. F. Kurgaev and A. V.
Palagin",
title = "On the question of the convergence of the {``digit by
digit''} methods of computing the elementary
functions",
journal = "Kibernetika (Kiev)",
volume = "4",
pages = "147--149",
year = "1974",
CODEN = "KBRNA5",
ISSN = "0023-1274",
MRclass = "65D20",
MRnumber = "53 \#1915",
MRreviewer = "V. V. Ivanov",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pomeranz:1974:AAE,
author = "John Pomeranz",
title = "{ACM Algorithm 487}: Exact Cumulative Distribution of
the {Kolmogorov--Smirnov} Statistic for Small Samples",
journal = j-CACM,
volume = "17",
number = "12",
pages = "703--704",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 07:12:56 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Pomeranz:1976:REC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Purdue Univ., West Lafayette, IN, USA",
keywords = "algorithm; exact cumulative distribution; FORTRAN;
Kolmogorov Smirnov test; natural sciences applications
of computers; small samples; statistic; statistics;
subroutines",
oldlabel = "Pomeranz74",
remark = "Fullerton: FORTRAN routine accurate apparently to 5
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Pomeranz74",
}
@Article{Sheorey:1974:CEW,
author = "V. B. Sheorey",
title = "{Chebyshev} Expansions for Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "7",
number = "1",
pages = "1--12",
month = jan,
year = "1974",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(74)90053-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:36:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Stegun:1974:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
{Part II}. {The} Exponential Integral {$E_n(x)$}",
journal = "J. Res. Nat. Bur. Stand.",
volume = "78B",
number = "4",
pages = "199--216",
month = oct,
year = "1974",
bibdate = "Sat Oct 30 11:00:40 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $E_n(x)$ and $e^x E_n(x)$.",
}
@Article{Wang:1974:UEZ,
author = "Paul S. Wang",
title = "The Undecidability of the Existence of Zeros of Real
Elementary Functions",
journal = j-J-ACM,
volume = "21",
number = "4",
pages = "586--589",
month = oct,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "From Richardson's undecidability results, it is shown
that the predicate ``there exists a real number such
that G(r) equals 0'' is recursively undecidable for
G(x) in a class of functions which involves polynomials
and the sine function. The deduction follows that the
convergence of a class of improper integrals is
recursively undecidable.",
acknowledgement = ack-nhfb,
classification = "921",
journalabr = "J Assoc Comput Mach",
keywords = "mathematical techniques",
}
@Article{Wimp:1974:CTP,
author = "J. Wimp",
title = "On the computation of {Tricomi}'s {Psi} function",
journal = j-COMPUTING,
volume = "13",
number = "3--4",
pages = "195--203",
year = "1974",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Drexel Univ., Philadelphia, PA, USA",
citedby = "Fullerton:1980:BEM",
classification = "723; 921; B0290D; C4120",
description = "convergence of numerical methods; function
evaluation",
journalabr = "Comput (Vienna/NY)",
keywords = "computation; computer programming --- Subroutines;
confluent hypergeometric function; convergence;
mathematical techniques; recurrence relations;
Tricomi's",
remark = "Fullerton: Backward recursion methods are discussed.",
}
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More efficient radix-$2$ algorithms for some
elementary functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1049--1054",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1975.224132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68A10",
MRnumber = "52 \#7193",
MRreviewer = "I. Kaufmann",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672725",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@Article{Baker:1975:PMA,
author = "P. W. Baker",
title = "Parallel Multiplicative Algorithms for Some Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "322--325",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1975.224215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672808",
abstract = "This correspondence presents generalized higher radix
algorithms for some elementary functions which use fast
parallel $m$-bit multipliers where $\mathrm{radix} =
2^m$. These algorithms are extensions of those
iterative schemes which are based on multiplications by
$(1 + 2^{-i})$ and the use of prestored values of $\ln
(1 + 2^{-i})$ and $\tan^{-1}(2^{-i})$. The particular
functions under consideration are $y/x$, $y/x^{1/2}$,
$y exp (x)$, $y + \ln (x)$, $\sin (x)$ and $\cos (x)$
[and hence $\tan (x)$]. The extended algorithms rely on
multiplication by $(1 + \mathrm{dir}^{-k})$ where
$\mathrm{dir}$, $0 \leq \mathrm{dir}$, is an $m$-bit
integer. Using a simple selection procedure for
$\mathrm{dir}$, simulations show that $p$ (radix $r$)
digits of a function may be generated, on the average,
in less than $p + 1$ iterations.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Boris:1975:NEO,
author = "Jay P. Boris and Elaine S. Oran",
title = "Numerical evaluation of oscillatory integrals such as
the modified {Bessel} function {$K_{i\zeta}(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "17",
number = "4",
pages = "425--433",
month = apr,
year = "1975",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(75)90045-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:17 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999175900455",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@TechReport{Brent:1975:MZM,
author = "R. P. (Richard P.) Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "26",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Iterative methods (Mathematics)",
searchkey = "ti:elementary n1 function",
}
@Article{Bujnowski:1975:EFC,
author = "G. Rudnicki Bujnowski",
title = "Explicit Formulas for {Clebsch--Gordan} Coefficients",
journal = j-COMP-PHYS-COMM,
volume = "10",
number = "4",
pages = "245--250",
month = oct,
year = "1975",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(75)90069-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:13:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465575900697",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
remark = "Fullerton: A PL/I-FORMAC procedure is discussed.",
}
@Article{Carta:1975:LOA,
author = "David G. Carta",
title = "Low-Order Approximations for the Normal Probability
Integral and the Error Function",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "856--862",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0260 (Optimisation techniques); B0290R (Integral
equations); C1180 (Optimisation techniques); C4180
(Integral equations)",
corpsource = "Jet Propulsion Lab., California Inst. of Technol.,
Pasadena, CA, USA",
keywords = "error function; fraction; integral equations; linear
minimax problems; linear programming; low; normal
probability integral; order approximations;
polynomials; rational",
treatment = "T Theoretical or Mathematical",
}
@Article{Cody:1975:FPS,
author = "W. J. Cody",
title = "The {FUNPACK} Package of Special Function
Subroutines",
journal = j-TOMS,
volume = "1",
number = "1",
pages = "13--25",
month = mar,
year = "1975",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355626.355631",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@PhdThesis{Epstein:1975:AET,
author = "Harvey Irwin Epstein",
title = "Algorithms for elementary transcendental function
arithmetic",
school = "University of Wisconsin",
address = "Madison, WI, USA",
pages = "409",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "Typescript. Vita. Thesis (Ph. D.)--University of
Wisconsin--Madison, 1975.",
keywords = "Algorithms.; Functions -- Data processing.; Functions,
Transcendental.",
searchkey = "ti:elementary n1 function",
}
@Article{Ferguson:1975:PFI,
author = "Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and
Grant Cook",
title = "A partition formula for the integer coefficients of
the theta function nome",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "851--855",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290R (Integral equations); C4180 (Integral
equations)",
corpsource = "Dept. of Math., Brigham Young Univ., Provo, UT, USA",
keywords = "coefficients; complete elliptic integrals; elliptic
function theory; elliptic integrals; incomplete;
integral equations; partition formula; theta function
nome integer",
remark = "Fullerton: Incomplete elliptic integrals can be
expressed as a series of theta functions.",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gargantini:1975:PSR,
author = "I. Gargantini",
editor = "K. Nickel",
booktitle = "Interval Mathematics",
title = "Parallel Square Root Iterations",
volume = "29",
publisher = pub-SV,
address = pub-SV:adr,
pages = "196--204",
year = "1975",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes In Computer Science",
acknowledgement = ack-jr,
}
@InProceedings{Gautschi:1975:CMS,
author = "W. Gautschi",
title = "Computational Methods in Special Functions --- {A}
Survey",
crossref = "Askey:1975:TAS",
pages = "1--98",
year = "1975",
bibdate = "Sat Oct 30 07:42:41 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Extensive list of references.",
}
@Article{Ginsberg:1975:AAD,
author = "E. S. Ginsberg and Dorothy Zaborowski",
title = "{ACM Algorithm 490}: The Dilogarithm Function of a
Real Argument [{S22}]",
journal = j-CACM,
volume = "18",
number = "4",
pages = "200--202",
month = apr,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 06:44:28 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#GinsbergZ75;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Morris:1976:RDF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "Dept. of Phys., Univ. of Massachusetts, Boston, MA,
USA",
keywords = "dilogarithm function; electrodynamics; ferromagnets;
function evaluation; function subroutine; ideal;
library; network analysis; polymers; quantum; real
argument; subprograms; subroutines; thermodynamics",
oldlabel = "GinsbergZ75",
remark = "Fullerton: FORTRAN routine accurate to 15 digits for
evaluating $\operatorname{Li}_2(x) = -\int_0^\infty
\frac{\ln(1 z)}{z} \, dz$.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GinsbergZ75",
}
@Article{Headley:1975:DZG,
author = "V. B. Headley and V. K. Barwell",
title = "On the distribution of the zeros of generalized {Airy}
functions",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "863--877",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "Dept. of Math., Brock Univ., St. Catherines, Ont.,
Canada",
keywords = "Bessel functions; boundary rays; differential
equations; generalized Airy functions; nonreal zeros;
zeros distribution",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Hitotumatu:1975:SRU,
author = "Sin Hitotumatu",
title = "Some remarks on the unified treatment of elementary
functions by microprogramming",
crossref = "Miller:1975:TNA",
pages = "51--56 (vol. 2)",
year = "1975",
MRclass = "65D15",
MRnumber = "54 \#11733",
MRreviewer = "Luciano Biasini",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ikebe:1975:ZRC,
author = "Yasuhiko Ikebe",
title = "The Zeros of Regular {Coulomb} Wave Functions and of
Their Derivatives",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "878--887",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Centre Numerical Analysis, Univ. of Texas, Austin, TX,
USA",
keywords = "Bessel function; compact matrix; eigenvalues;
eigenvalues and eigenfunctions; function zeros
characterisation; matrix algebra; methods; numerical;
operators; regular Coulomb wave functions; wave
functions; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Kioustelidis:1975:PLA,
author = "J. B. Kioustelidis and J. K. Petrou",
title = "A Piecewise Linear Approximation of $\log_2 x$ with
Equal Maximum Errors in All Intervals",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "9",
pages = "858--861",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1975.224330",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672923",
abstract = "In this paper it is shown how to divide the interval
$[1,2]$ into $n$ parts so that the uniform linear
approximation of $\log_2 x$ in each subinterval has the
same maximum error. This error is, in the case $n = 4$,
smaller by a factor of $2.3$ than the error of the
linear mean-square approximation given by Hall et al.
[1]. The final products of the mathematical analysis
are explicit formulas which allow the direct
determination of all parameters and the maximum error
for any desired number $n$ of subdivisions of
$[1,2]$.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
keywords = "$\log_2(x)$; elementary function",
}
@Article{Lewis:1975:CPF,
author = "John Gregg Lewis",
title = "Certification of ``{Algorithm} 349: Polygamma
Functions with Arbitrary Precision''",
journal = j-TOMS,
volume = "1",
number = "4",
pages = "380--382",
month = dec,
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Jun 16 10:31:40 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{TadeudeMedeiros:1969:APF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "polygamma functions; special functions",
}
@Article{Midy:1975:ICG,
author = "P. Midy",
title = "An improved calculation of the general elliptic
integral of the second kind in the neighbourhood of $x
= 0$",
journal = j-NUM-MATH,
volume = "25",
number = "1",
pages = "99--101",
month = mar,
year = "1975",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Centre de Calcul Paris Sud Informatique, Univ. Paris
XI, Orsay, France",
keywords = "elliptic integral; integration; Landen transformation;
second kind",
treatment = "T Theoretical or Mathematical",
}
@Article{Ng:1975:CCM,
author = "Edward W. Ng",
title = "A Comparison of Computational Methods and Algorithms
for the Complex Gamma Function",
journal = j-TOMS,
volume = "1",
number = "1",
pages = "56--70",
month = mar,
year = "1975",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355626.355635",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20",
MRnumber = "52 #2148",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
reviewer = "R. H. Bartels",
}
@Article{Prince:1975:AAF,
author = "P. J. Prince",
title = "{Algorithm 498}: {Airy} Functions Using {Chebyshev}
Series Approximations",
journal = j-TOMS,
volume = "1",
number = "4",
pages = "372--379",
month = dec,
year = "1975",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355656.355663",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 00:24:33 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Razaz:1981:RAF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: FORTRAN routines of fixed 10D precision for
the two Airy functions and their derivatives are
given.",
}
@Article{Skovgaard:1975:RAJ,
author = "Ove Skovgaard",
title = "Remark on ``{Algorithm 332}: {Jacobi} Polynomials''",
journal = j-CACM,
volume = "18",
number = "2",
pages = "116--117",
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Mon Jan 22 07:22:18 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Skovgaard75;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Witte:1968:AAJ}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
oldlabel = "Skovgaard75",
remark = "Fullerton: Modifications to an adjustable-precision
FORTRAN routine.",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Skovgaard75",
}
@Article{Temme:1975:NEM,
author = "N. M. Temme",
title = "On the Numerical Evaluation of the Modified {Bessel}
Function of the Third Kind",
journal = j-J-COMPUT-PHYS,
volume = "19",
number = "3",
pages = "324--337",
month = nov,
year = "1975",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(75)90082-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 11:20:31 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
}
@Article{Temme:1975:UAE,
author = "N. M. Temme",
title = "Uniform asymptotic expansions of the incomplete gamma
functions and the incomplete beta function",
journal = j-MATH-COMPUT,
volume = "29",
number = "132",
pages = "1109--1114",
month = oct,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Appl. Math., Amsterdam, Netherlands",
keywords = "asymptotic expansions; asymptotic series;
complementary error function; function approximation;
incomplete beta function; incomplete gamma functions;
uniform",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Warner:1975:PDG,
author = "D. D. Warner",
title = "A partial derivative generator",
type = "Computing Science Technical Report",
number = "28",
institution = "Bell Telephone Laboratories",
address = "Murray Hill, NJ, USA",
year = "1975",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Theory/auto.diff.bib",
abstract = "A precompiler is described which takes a specification
of a function as input and produces a Fortran
subroutine which will evaluate the component functions
and the corresponding Jacobian. Many of the Fortran
elementary functions are provided, as well as a
facility which allows the user to specify their own
differentiation rules.",
acknowledgement = ack-nhfb,
keywords = "differentiation arithmetic; precompiler.",
referred = "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
}
@Article{Assmus:1976:NFS,
author = "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
Howard E. Sachar",
title = "A New Form of the Square Root Bound",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "2",
pages = "352--354",
month = mar,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Lehigh Univ., Bethlehem, PA, USA",
fjournal = "SIAM Journal on Applied Mathematics",
keywords = "combinatorial mathematics; linear codes; square root
bound; sufficient combinatorial conditions",
treatment = "T Theoretical or Mathematical",
}
@Article{Baker:1976:SFB,
author = "P. W. Baker",
title = "Suggestion for a fast binary sine\slash cosine
generator",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1134--1136",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1976.1674566",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:55 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674566",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
keywords = "$\cos(x)$; $\sin(x)$; elementary function",
}
@Article{Barnett:1976:MRC,
author = "A. R. Barnett",
title = "{RCWFF} --- Modification of the Real {Coulomb}
Wavefunction Program {RCWFN}",
journal = j-COMP-PHYS-COMM,
volume = "11",
number = "1",
pages = "141--142",
month = jan # "\slash " # feb,
year = "1976",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(76)90045-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:24:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Blair:1976:RCA,
author = "J. M. Blair and C. A. Edwards and J. H. Johnson",
title = "Rational {Chebyshev} approximations for the inverse of
the error function",
journal = j-MATH-COMPUT,
volume = "30",
number = "136",
pages = "827--830",
month = oct,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy of Canada Ltd., Chalk River Nuclear
Lab., Chalk River, Ont., Canada",
keywords = "Chebyshev approximation; Chebyshev approximations;
error function; inverse; rational",
remark = "Fullerton: With microfiche supplement.",
treatment = "T Theoretical or Mathematical",
}
@Article{Brent:1976:FMP,
author = "Richard P. Brent",
title = "Fast Multiple-Precision Evaluation of Elementary
Functions",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "242--251",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/321941.321944",
ISSN = "0004-5411",
MRclass = "68A20 (68A10)",
MRnumber = "52 \#16111",
MRreviewer = "Amnon Barak",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Let $f(x)$ be one of the usual elementary functions
($\exp$, $\log$, $\artan$, $\sin$, $\cosh$, etc.), and
let $M(n)$ be the number of single-precision operations
required to multiply $n$-bit integers. It is shown that
$f(x)$ can be evaluated, with relative error $O(2-n)$,
in $O(M(n)log (n))$ operations as $n \rightarrow
\infty$, for any floating-point number $x$ (with an
$n$-bit fraction) in a suitable finite interval. From
the Sch{\"o}nhage--Strassen bound on $M(n)$, it follows
that an $n$-bit approximation to $f(x)$ may be
evaluated in $O(n \log_(n) \log \log(n))$ operations.
Special cases include the evaluation of constants such
as $\pi$ $e$, and $e^\pi$. The algorithms depend on the
theory of elliptic integrals, using the
arithmetic-geometric mean iteration and ascending
Landen transformations.",
acknowledgement = ack-nhfb,
classification = "723",
journalabr = "J Assoc Comput Mach",
keywords = "computational complexity; computer arithmetic;
computer programming",
}
@InProceedings{Brent:1976:MPZ,
author = "Richard P. Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
crossref = "Traub:1976:ACC",
pages = "151--176",
year = "1976",
MRclass = "68A20",
MRnumber = "54 \#11843",
MRreviewer = "Claus-Peter Schnorr",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Buschman:1976:IHF,
author = "R. G. Buschman",
title = "Inequalities for Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "30",
number = "134",
pages = "303--305",
month = apr,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math. and Statistics, Univ. of Guelph,
Guelph, Ont., Canada",
keywords = "Bessel functions; classical orthogonal polynomials;
confluence; dominant diagonal matrix; function;
functions; Gauss' hypergeometric; hypergeometric
functions; Kummer's hypergeometric function; modified
Bessel function; principle",
treatment = "T Theoretical or Mathematical",
}
@Article{Davies:1976:IPS,
author = "M. Davies and B. Dawson",
title = "The incrementation parameter in square root
iteration",
journal = j-J-INST-MATH-APPL,
volume = "17",
number = "2",
pages = "219--223",
year = "1976",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65H05",
MRnumber = "55 #9514",
MRreviewer = "Luciano Biasini",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
ZMnumber = "0319.65039",
}
@Article{Deuflhard:1976:ASC,
author = "P. Deuflhard",
title = "On Algorithms for the Summation of Certain Special
Functions",
journal = j-COMPUTING,
volume = "17",
number = "1",
pages = "37--48",
year = "1976",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Inst. f{\"u}r Math., Tech. Univ. M{\"u}nchen,
M{\"u}nchen, West Germany",
citedby = "Fullerton:1980:BEM",
classification = "723; 921; B0290B; B0290H; C4110; C4140",
description = "error analysis; linear algebra",
journalabr = "Comput (Vienna/NY)",
keywords = "algorithms; backward error analysis; computer
programming; graph representation; mathematical
techniques; special functions; stability; summation",
remark = "Fullerton: An extension of Clenshaw's summation method
is discussed. Spherical harmonic sums are considered as
a special case.",
}
@Article{Eckhardt:1976:RAW,
author = "Ulrich Eckhardt",
title = "A Rational Approximation to {Weierstrass}'
$\wp$-Function",
journal = j-MATH-COMPUT,
volume = "30",
number = "136",
pages = "818--826",
month = oct,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); C4130
(Interpolation and function approximation)",
corpsource = "Nuclear Res. Center, Central Inst. for Appl. Math.,
Julich, West Germany",
keywords = "equianharmonic; function approximation; rational
approximation; unit period parallelogram; Weierstrass'
elliptic function; Weierstrass' p function",
remark = "Fullerton: A complex FORTRAN algorithm with accuracy
down to $10^{-18}$ is given.",
treatment = "T Theoretical or Mathematical",
}
@Article{Ellacott:1976:RCA,
author = "S. Ellacott and Jack Williams",
title = "Rational {Chebyshev} Approximation in the Complex
Plane",
journal = j-SIAM-J-NUMER-ANAL,
volume = "13",
number = "3",
pages = "310--323",
month = jun,
year = "1976",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{elLozy:1976:RAC,
author = "Mohamed el Lozy",
title = "Remark on {``Algorithm 299: Chi-Squared Integral
[S15]''}",
journal = j-TOMS,
volume = "2",
number = "4",
pages = "393--395",
month = dec,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Jul 05 16:47:38 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1967:ACS,Hill:1985:RCS}.",
acknowledgement = ack-nhfb,
}
@Article{Fettis:1976:CR,
author = "Henry E. Fettis",
title = "Complex Roots of $\sin z = az, \cos z = az$, and
$\cosh z = az$",
journal = j-MATH-COMPUT,
volume = "30",
number = "135",
pages = "541--545",
month = jul,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
keywords = "complex roots; cos z=az; cosh z=az; functional
equations; sin z=az",
treatment = "T Theoretical or Mathematical",
}
@Article{Fullerton:1976:AEM,
author = "L. W. Fullerton and G. A. {Rinker, Jr.}",
title = "Accurate and Efficient Methods for the Evaluation of
Vacuum-Polarization Potentials of Order {$Z\alpha$} and
{$Z\alpha^2$}",
journal = j-PHYS-REV-A,
volume = "13",
number = "3",
pages = "1283--1287",
month = mar,
year = "1976",
CODEN = "PLRAAN",
ISSN = "1050-2947",
bibdate = "Sat Oct 30 06:32:26 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Nine-figure approximations to $K_n(x) =
\int_1^\infty e^{-x t} t^n (1/r^3 + 1/(2 r^5)) (r^2 -
1)^{1/2} \, dt$ for $n = 0, 1, 3$, and $5$.",
}
@Article{Kononova:1976:CEF,
author = "N. F. Kononova",
title = "The computation of elementary functions by means of
polynomial approximations by the method of {V. K.
Dzjadik}. ({Russian})",
journal = "Vy{\v{c}}isl. Prikl. Mat. (Kiev)",
volume = "29",
pages = "27--39",
year = "1976",
ISSN = "0321-4117",
MRclass = "151. 65D15",
MRnumber = "57 \#18026",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lentz:1976:GBF,
author = "W. G. Lentz",
title = "Generating {Bessel} Functions in {Mie} Scattering
Calculations Using Continued Fractions",
journal = j-APPL-OPTICS,
volume = "15",
number = "3",
pages = "668--671",
month = mar,
year = "1976",
CODEN = "APOPAI",
ISSN = "0003-6935",
bibdate = "Sat Oct 30 08:41:40 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Morris:1976:RDF,
author = "Robert Morris",
title = "Remark on ``{Algorithm 490}: The Dilogarithm Function
of a Real Argument [{S22}]''",
journal = j-TOMS,
volume = "2",
number = "1",
pages = "112--112",
month = mar,
year = "1976",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355666.355680",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Aug 30 00:27:18 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Ginsberg:1975:AAD}.",
acknowledgement = ack-nhfb,
}
@Article{Paul:1976:SEF,
author = "George Paul and M. Wayne Wilson",
title = "Should the Elementary Function Library Be Incorporated
Into Computer Instruction Sets?",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "132--142",
month = jun,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 00:30:21 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pike:1976:RIB,
author = "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten",
title = "Remark on {``Algorithm 179: Incomplete Beta Ratio
[S14]''}",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "207--208",
month = jun,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Jul 05 16:45:39 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Ludwig:1963:AIB,Bosten:1974:RAI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Pomeranz:1976:REC,
author = "J. Pomeranz",
title = "Remark on ``{Algorithm 487: Exact Cumulative
Distribution of the Kolmogorov--Smirnov Statistic for
Small Samples [S14]}''",
journal = j-TOMS,
volume = "2",
number = "1",
pages = "111--111",
month = mar,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:05 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Pomeranz:1974:AAE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Redding:1976:CPC,
author = "R. W. Redding and W. P. Latham",
title = "On the calculation of the parabolic cylinder
functions. {II}. {The} function {$V(a,x)$}",
journal = j-J-COMPUT-PHYS,
volume = "20",
number = "2",
pages = "256--258",
month = feb,
year = "1976",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(76)90071-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:20 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999176900711",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Salamin:1976:CUA,
author = "Eugene Salamin",
title = "Computation of $\pi$ Using Arithmetic-Geometric Mean",
journal = j-MATH-COMPUT,
volume = "30",
number = "135",
pages = "565--570",
month = jul,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Charles Stark Draper Lab., Cambridge, MA, USA",
keywords = "arithmetic geometric mean; convergence; elliptic
integrals; error analysis; fast Fourier transform
multiplication; function evaluation; Landen's;
Legendre's relation; numerical computation of pi;
transformation",
remark = "Fullerton: A quadratically convergent algorithm.",
treatment = "A Application; T Theoretical or Mathematical",
}
@InCollection{Salimov:1976:OCE,
author = "F. I. Salimov",
booktitle = "Probabilistic methods and cybernetics",
title = "The organization of calculations of elementary
functions into tables. ({Russian})",
volume = "12--13",
publisher = "Kazan University",
address = "Kazan, USSR",
pages = "77--90",
year = "1976",
MRclass = "65A05",
MRnumber = "58 \#31706",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Schett:1976:PTS,
author = "Alois Schett",
title = "Properties of the {Taylor} series expansion
coefficients of the {Jacobian} elliptic functions",
journal = j-MATH-COMPUT,
volume = "30",
number = "133",
pages = "143--147",
month = jan,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "CENS, Gif-sur-Yvette, France",
keywords = "differential equations; Jacobian elliptic functions;
randomisation distributions; series (mathematics);
Taylor series expansion",
remark = "Fullerton: The first several coefficients are
tabulated.",
treatment = "T Theoretical or Mathematical",
}
@Article{Schonfelder:1976:PSF,
author = "J. L. Schonfelder",
title = "The Production of Special Function Routines for a
Multi-Machine Library",
journal = j-SPE,
volume = "6",
number = "1",
pages = "71--82",
month = jan # "\slash " # mar,
year = "1976",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The design of transportable routines for
the NAG library is discussed.",
}
@Article{Schulten:1976:REC,
author = "K. Schulten and R. G. Gordon",
title = "Recursive Evaluation of $3j$ and $6j$ Coefficients",
journal = j-COMP-PHYS-COMM,
volume = "11",
number = "2",
pages = "269--278",
month = mar # "\slash " # may,
year = "1976",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(76)90058-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:32:44 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Sheorey:1976:DCE,
author = "V. B. Sheorey",
title = "Double {Chebyshev} Expansions for Wave Functions",
journal = j-COMP-PHYS-COMM,
volume = "12",
number = "2",
pages = "125--134",
month = nov,
year = "1976",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(76)90061-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:38:43 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465576900618",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Siemieniuch:1976:PCR,
author = "J. L. Siemieniuch",
title = "Properties of certain rational approximations to
$e^{-z}$",
journal = j-BIT,
volume = "16",
number = "2",
pages = "172--191",
month = jun,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931369",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172",
acknowledgement = ack-nhfb,
keywords = "elefunt; elementary functions",
}
@Article{Stegun:1976:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
{Part III}. {The} Sine, Cosine, Exponential Integrals,
and Related Functions",
journal = "J. Res. Nat. Bur. Stand.",
volume = "80B",
number = "2",
pages = "291--311",
month = apr,
year = "1976",
bibdate = "Sat Oct 30 11:07:19 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Adjustable double precision FORTRAN.
routines for $\operatorname{Si}$, $\operatorname{Ci}$,
$\operatorname{Ei}$, $\operatorname{Shi}$, and
$\operatorname{Chi}$.",
}
@Article{Temme:1976:NEO,
author = "Nico M. Temme",
title = "On the numerical evaluation of the ordinary {Bessel}
function of the second kind",
journal = j-J-COMPUT-PHYS,
volume = "21",
number = "3",
pages = "343--350",
month = jul,
year = "1976",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(76)90032-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:21 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999176900322",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Tugov:1976:MCA,
author = "I. I. Tugov and Yu. L. Shitkov",
title = "A Method of Calculating the {Appell} Functions
${F}_a(\alpha; \beta, \beta'; \gamma; x, y)$",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "16",
number = "6",
pages = "1587--1590",
year = "1976",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
bibdate = "Sat Oct 30 11:38:05 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: [English] translation of Russian-language
Zhurnal Vychislitel'noi Matematikii Matemancheskoi
Fiziki (1976).",
}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Routine",
journal = j-IBM-TDB,
volume = "20",
number = "3",
pages = "1222",
month = aug,
year = "1977",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Amos:1977:ACS,
author = "D. E. Amos and S. L. Daniel and M. K. Weston",
title = "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and
{JBESS} for {Bessel} Functions {$I_\nu(x)$} and
{$J_\nu(x)$}, {$x \ge 0, \nu \ge 0$} [{S18}]",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "93--95",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355719.355727",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Thu Apr 29 15:14:12 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Amos:1978:ECS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Amos:1977:CSI,
author = "D. E. Amos and S. L. Daniel and M. K. Weston",
title = "{CDC} 6600 Subroutines {IBESS} and {JBESS} for
{Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$},
{$x\ge0,\nu\ge0$}",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "76--92",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355719.355726",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20",
MRnumber = "55 #6781",
bibdate = "Tue Sep 06 19:20:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
reviewer = "Sven-{\AA}ke Gustafson",
}
@Article{Ardill:1977:BFC,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "The {Bessel} Functions {$J_0$} and {$J_1$} of Complex
Argument",
journal = j-COMP-PHYS-COMM,
volume = "13",
number = "1",
pages = "17--24",
month = may,
year = "1977",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(77)90023-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:19:09 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465577900236",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Book{Brezinski:1977:ACA,
author = "Claude Brezinski",
title = "Acc{\'e}l{\'e}ration de la convergence en analyse
num{\'e}rique. ({French}) [{Convergence} acceleration
in numerical analysis]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "313",
year = "1977",
ISBN = "0-387-08241-7, 3-540-08241-7",
ISBN-13 = "978-0-387-08241-7, 978-3-540-08241-5",
LCCN = "????",
bibdate = "Thu Dec 1 10:17:17 MST 2011",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "French",
}
@Article{Carlson:1977:EIF,
author = "B. C. Carlson",
title = "Elliptic Integrals of the First Kind",
journal = j-SIAM-J-MATH-ANA,
volume = "8",
number = "2",
pages = "231--242",
month = "????",
year = "1977",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRnumber = "MR 0430341 (55:3346)",
bibdate = "Fri Oct 29 22:03:28 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Carlson:1977:SFA,
author = "Bille Chandler Carlson",
title = "Special Functions of Applied Mathematics",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 335",
year = "1977",
ISBN = "0-12-160150-1",
ISBN-13 = "978-0-12-160150-8",
LCCN = "QA351 .C32",
bibdate = "Fri Jan 22 10:33:57 MST 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special",
}
@Article{Cody:1977:CRF,
author = "W. J. Cody and Rose M. Motley and L. Wayne Fullerton",
title = "The Computation of Real Fractional Order {Bessel}
Functions of the Second Kind",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "232--239",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355744.355747",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Sep 20 18:24:22 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Danilcenko:1977:ETC,
author = "L. S. Danil'{\v{c}}enko",
title = "An efficient technique for the construction of
rational approximations of elementary functions.
({Russian}) Optimization of computations (approximation
and minimization of functions)",
journal = "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint",
volume = "18",
pages = "17--21",
year = "1977",
MRclass = "65D15",
MRnumber = "80b:65016",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dijkstra:1977:CFE,
author = "D. Dijkstra",
title = "A continued fraction expansion for a generalization of
{Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "31",
number = "138",
pages = "503--510",
month = apr,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods); C4120
(Functional analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math., Tech. Univ. Twente, Enschede,
Netherlands",
keywords = "confluent hypergeometric; continued fraction
expansion; Dawson's; error analysis; function; function
evaluation; generalization; integral; integration;
truncation error",
remark = "Fullerton: An expansion for $F(p, x) = e^{-x^2}
\int_0^x e^{t^2} \, dt$ is given.",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Dzjadyk:1977:TPA,
author = "V. K. Dzjadyk and S. F. Karpenko",
title = "Tables of polynomials for the approximate solution of
elementary functions. ({Russian})",
number = "28",
institution = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
pages = "28",
year = "1977",
MRclass = "65A05 (65D20)",
MRnumber = "58 \#19016",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Dzyadyk:1977:OPM,
author = "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko
and N. F. Kononova",
title = "{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami
{\`e}lementarnykh funktsi{\u{\i}}.} ({Russian})
[Efficient approximation by polynomials of elementary
functions]",
type = "Preprint",
number = "IM-77-21",
institution = "Akad. Nauk Ukrain. SSR Inst. Mat.",
address = "Kiev, USSR",
pages = "42",
year = "1977",
MRclass = "65L99",
MRnumber = "57 \#11075",
MRreviewer = "B. D. Donevski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Eckhardt:1977:RAW,
author = "Ulrich Eckhardt",
title = "A rational approximation to {Weierstrass}' elliptic
function. {II}. {The} lemniscatic case",
journal = j-COMPUTING,
volume = "18",
number = "4",
pages = "341--349",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Zentralinst. f{\"u}r Angewandte Math., Julich, West
Germany",
citedby = "Fullerton:1980:BEM",
classification = "C4130",
description = "function approximation",
keywords = "elliptic functions; lemniscatic case; rational
approximation; Weierstrass elliptic function",
remark = "Fullerton: Weierstrass' function and its derivative
are approximated in the complex plane to 16 S.",
}
@Article{Egbert:1977:PCAa,
author = "W. E. Egbert",
title = "Personal calculator algorithms. {I}. Square roots",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "9",
pages = "22--23",
month = may,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
keywords = "electronic calculators; HP personal calculator; square
root algorithm",
treatment = "A Application; T Theoretical or Mathematical",
xxpages = "22--24",
}
@InProceedings{Fullerton:1977:PSF,
author = "L. W. Fullerton",
title = "Portable Special Function Routines",
crossref = "Cowell:1977:PMS",
pages = "452--483",
year = "1977",
bibdate = "Sat Oct 30 06:40:00 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Gautschi:1977:ACC,
author = "Walter Gautschi",
title = "Anomalous convergence of a continued fraction for
ratios of {Kummer} functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "140",
pages = "994--999",
month = oct,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4170 (Differential
equations)",
corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
USA",
keywords = "apparent; Bessel functions; continued fraction;
convergence; differential equations; gamma functions;
Kummer functions; wrong limit",
treatment = "T Theoretical or Mathematical",
}
@Article{Gautschi:1977:ERI,
author = "Walter Gautschi",
title = "Evaluation of Repeated Integrals of the Coerror
Function",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "240--252",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355744.355748",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 22:26:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: An arbitrary-accuracy method for evaluating
$i^n \erfc(x)$ is given.",
}
@Article{Harris:1977:CAT,
author = "F. E. Harris",
title = "Convergence acceleration technique for lattice sums
arising in electronic-structure studies of crystalline
solids",
journal = j-J-MATH-PHYS,
volume = "18",
number = "12",
pages = "2377--2381",
month = dec,
year = "1977",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
bibdate = "Fri Jan 2 14:59:17 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "A0260 (Numerical approximation and analysis); A6150L
(Crystal binding)",
corpsource = "Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA",
keywords = "convergence acceleration; convergence of numerical
methods; crystalline solids; electronic structure;
Laplace transform; Laplace transforms; lattice energy;
lattice sums; Poisson's summation formula",
pubcountry = "USA",
treatment = "T Theoretical or Mathematical",
}
@Book{Higgins:1977:CBP,
author = "John Rowland Higgins",
title = "Completeness and basis properties of sets of special
functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 134",
year = "1977",
ISBN = "0-521-21376-2 (hardcover), 0-521-60488-5 (paperback)",
ISBN-13 = "978-0-521-21376-9 (hardcover), 978-0-521-60488-8
(paperback)",
LCCN = "????",
bibdate = "Sat Oct 30 16:52:55 MDT 2010",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1977:AIB,
author = "G. W. Hill",
title = "{Algorithm 518}: Incomplete {Bessel} Function {$I_0$}.
{The von Mises} Distribution [{S14}]",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "279--284",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355744.355753",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Oct 24 15:46:06 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Adjustable-accuracy 50-statement FORTRAN
subprogram.",
}
@Article{Hinden:1977:PAR,
author = "Harvey J. Hinden",
title = "Phi Again: a Relationship Between the Golden Ratio and
the Limit of a Ratio of Modified {Bessel} Functions",
journal = j-FIB-QUART,
volume = "15",
number = "2",
pages = "112, 152",
month = apr,
year = "1977",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:17 MDT 2011",
bibsource = "http://www.fq.math.ca/15-2.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Ismail:1977:IRC,
author = "Mourad E. H. Ismail",
title = "Integral representations and complete monotonicity of
various quotients of {Bessel} functions",
journal = j-CAN-J-MATH,
volume = "29",
number = "??",
pages = "1198--1207",
month = "????",
year = "1977",
CODEN = "CJMAAB",
DOI = "http://dx.doi.org/10.4153/CJM-1977-119-5",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:50 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v29/;
http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
}
@Article{Jansen:1977:RLF,
author = "J. K. M. Jansen",
title = "Remark on ``{Algorithm 259: Legendre Functions for
Arguments Larger than One}''",
journal = j-TOMS,
volume = "3",
number = "2",
pages = "204--250",
month = jun,
year = "1977",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:08 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1965:ALF}.",
acknowledgement = ack-nhfb,
}
@Book{Luke:1977:ACM,
author = "Yudell L. Luke",
title = "Algorithms for the Computation of Mathematical
Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 284",
year = "1977",
ISBN = "0-12-459940-0",
ISBN-13 = "978-0-12-459940-6",
LCCN = "QA351 .L7961",
bibdate = "Wed Dec 15 10:38:19 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
wrongisbn = "0-12-459940-6",
}
@Article{Marsaglia:1977:SMG,
author = "George Marsaglia",
title = "The squeeze method for generating gamma variates",
journal = j-COMP-MATH-APPL,
volume = "3",
number = "4",
pages = "321--325",
year = "1977",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(77)90089-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65C10",
MRnumber = "58 \#13613",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
abstract = "This paper describes an exact method for computer
generation of random variables with a gamma
distribution. The method is based on the
Wilson--Hilferty transformation and an improvement on
the rejection technique. The idea is to ``squeeze'' a
target density between two functions, the top one easy
to sample from, the bottom one easy to evaluate.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
ZMclass = "*65C10 Random number generation 60E05 General theory
of probability distributions",
ZMnumber = "0384.65005",
}
@Article{Martins:1977:DSB,
author = "Pedro de A. P. Martins",
title = "Determination of spherical {Bessel}'s functions of an
order larger than the argument",
journal = j-J-COMPUT-PHYS,
volume = "25",
number = "2",
pages = "194--198",
month = oct,
year = "1977",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(77)90021-3",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999177900213",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{McCarthy:1977:OAE,
author = "D. P. McCarthy",
title = "The optimal algorithm to evaluate $x^n$ using
elementary multiplication methods",
journal = j-MATH-COMPUT,
volume = "31",
number = "137",
pages = "251--256",
month = jan,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis); C4240 (Programming and
algorithm theory)",
keywords = "computational complexity; function evaluation; optimal
multiplication chains; symbolic algebraic
manipulation",
treatment = "T Theoretical or Mathematical",
}
@Article{Ng:1977:CAL,
author = "E. W. Ng",
title = "Computations and Applications of Linear Hypergeometric
Transformations",
journal = j-COMP-MATH-APPL,
volume = "3",
number = "1",
pages = "65--70",
year = "1977",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(77)90115-8",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sat Oct 30 09:27:55 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Linear transformations are well-known in the theory of
hypergeometric functions. In this note, it is
indicated, both by analyses and by supporting numerical
experiments, how these transformations can be applied
to the computation of Legendre's functions, the
incomplete Beta function, and the variance-ratio
probability distribution function. It is shown that a
simple transformation can in many cases cause dramatic
improvement in computation.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Pexton:1977:RTTa,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Roots of two transcendental equations involving
spherical {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "139",
pages = "752--753",
month = jul,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Univ. of California, Livermore, CA, USA",
keywords = "Bessel functions; root; spherical Bessel functions;
transcendental equations",
treatment = "T Theoretical or Mathematical",
}
@Article{Schett:1977:RFT,
author = "Alois Schett",
title = "Recurrence formula of the {Taylor} series expansion
coefficients of the {Jacobian} elliptic functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "140",
pages = "1003--1005",
month = oct,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1110 (Algebra)",
corpsource = "CENS, Gif-sur-Yvette, France",
keywords = "elliptic functions; functions; Jacobian elliptic;
peak; recurrence formula; run up; Taylor series
expansion coefficients",
treatment = "T Theoretical or Mathematical",
}
@Article{Schindler:1977:CCS,
author = "Susan Schindler and R. Mirman",
title = "The {Clebsch--Gordan} coefficients of {$S_n$}",
journal = j-J-MATH-PHYS,
volume = "18",
number = "8",
pages = "1697--1704",
month = aug,
year = "1977",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.523470",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
bibdate = "Fri Jan 2 14:59:17 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Ordering schemes for the frames and tableaux of $S_n$
are presented, and some results, expressible in terms
of these, are developed. A formula is derived for the
sign function on tableaux. A table of the nonzero
Clebsch--Gordon coefficients for the ''working
triplets'' is given. Methods are described, and a
needed table supplied, for finding the other
coefficients from the tabulated ones. The values are
for $n = 2, \ldots{}, 6$, with the coefficients for $n
= 6$ relegated to PAPS.",
acknowledgement = ack-nhfb,
classification = "A0365F (Algebraic methods in quantum theory); A1130L
(Other internal and higher symmetries in particle
physics)",
corpsource = "Baruch Coll., City Univ. of New York, NY, USA",
keywords = "$S_n$ group; Clebsch Gordan coefficients;
Clebsch--Gordan coefficients; working triplets",
pubcountry = "USA",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Schonfelder:1977:PTS,
author = "J. L. Schonfelder",
title = "The Production and Testing of Special Function
Software in the {NAG} Library",
crossref = "Cowell:1977:PMS",
pages = "425--451",
year = "1977",
bibdate = "Sat Oct 30 10:24:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Sharma:1977:GMA,
author = "R. R. Sharma and Bahman Zohuri",
title = "A general method for an accurate evaluation of
exponential integrals {$E_1(x), x > 0$}",
journal = j-J-COMPUT-PHYS,
volume = "25",
number = "2",
pages = "199--204",
month = oct,
year = "1977",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(77)90022-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999177900225",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Verma:1977:CSF,
author = "Arun Verma",
title = "Certain summation formulae for basic hypergeometric
series",
journal = j-CAN-MATH-BULL,
volume = "20",
number = "??",
pages = "369--376",
month = "????",
year = "1977",
CODEN = "CMBUA3",
DOI = "http://dx.doi.org/10.4153/CMB-1977-055-8",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
bibdate = "Thu Sep 8 10:04:41 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v20/;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
}
@Article{Amos:1978:ECS,
author = "Donald E. Amos",
title = "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
{IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$}
and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$} [{S18}]''",
journal = j-TOMS,
volume = "4",
number = "4",
pages = "411--411",
month = dec,
year = "1978",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/356502.356501",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Aug 30 00:28:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Amos:1977:ACS}.",
acknowledgement = ack-nhfb,
}
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
title = "Evaluation of Functions on Microcomputers: Square
Root",
journal = j-COMP-MATH-APPL,
volume = "4",
number = "4",
pages = "359--367",
year = "1978",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:29 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
}
@Article{Andrews:1978:UEF,
author = "M. Andrews and T. Mraz",
title = "Unified elementary function generator",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "270--273",
month = oct,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Ardill:1978:SBF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Spherical {Bessel} functions $j_n$ and $y_n$ of
integer order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "14",
number = "3--4",
pages = "261--265",
month = may # "\slash " # jun,
year = "1978",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(78)90019-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001046557890019X",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Benton:1978:CZT,
author = "T. C. Benton and H. D. Knoble",
title = "Common Zeros of Two {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "142",
pages = "533--535",
month = apr,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Pennsylvania State Univ., University Park, PA, USA",
keywords = "Bessel functions; common zeros; poles and zeros;
positive zeros; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Blair:1978:RCA,
author = "J. M. Blair and C. A. Edwards and J. H. Johnson",
title = "Rational {Chebyshev} approximations for the {Bickley}
functions {$Ki_n(x)$}",
journal = j-MATH-COMPUT,
volume = "32",
number = "143",
pages = "876--886",
month = jul,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy of Canada Ltd., Chalk River, Ont.,
Canada",
keywords = "approximation; Bessel functions; Bickley functions;
Chebyshev approximation; Chebyshev approximations;
function; recurrence; relation",
remark = "Fullerton: Approximations accurate to 23 digits of
repeated integrals of the Bessel function $K_0(x)$ for
$n = 1, 2, \ldots{}, 10$.",
treatment = "T Theoretical or Mathematical",
}
@Book{Brezinski:1978:AAC,
author = "Claude Brezinski",
title = "Algorithmes d'acc{\'e}l{\'e}ration de la convergence:
{\'e}tude num{\'e}rique. ({French}) [Algorithms for
convergence acceleration: numerical study]",
publisher = "{\'E}ditions Technip",
address = "Paris, France",
pages = "xi + 392",
year = "1978",
ISBN = "2-7108-0341-0 (paperback)",
ISBN-13 = "978-2-7108-0341-6 (paperback)",
LCCN = "????",
bibdate = "Thu Dec 1 10:20:23 MST 2011",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Brezinski:1978:CAS,
author = "C. Brezinski",
title = "Convergence acceleration of some sequences by the
$\epsilon$-algorithm",
journal = j-NUM-MATH,
volume = "29",
number = "2",
pages = "173--177",
month = jan,
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve
d'Ascq, France",
fjournal = "Numerische Mathematik",
keywords = "acceleration; converge; convergence acceleration;
convergence of numerical methods; epsilon-algorithm;
sequences",
treatment = "T Theoretical or Mathematical",
}
@Article{Brezinski:1978:SCA,
author = "C. Brezinski",
title = "Survey on convergence acceleration methods in
numerical analysis",
journal = "Math. Student",
volume = "46",
number = "1",
pages = "28--41 (1979)",
year = "1978",
CODEN = "MTHSBH",
ISSN = "0025-5742",
MRclass = "65B99",
MRnumber = "698176 (84d:65003)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematics Student",
keywords = "convergence acceleration",
}
@Article{Chin:1978:DAD,
author = "R. C. Y. Chin and G. W. Hedstrom",
title = "A dispersion analysis for difference schemes: tables
of generalized {Airy} functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1163--1170",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
corpsource = "Univ. of California, Lawrence Livermore Lab.,
Livermore, CA, USA",
keywords = "artificial viscosity; difference schemes; dispersion
analysis; function approximation; functions;
generalized Airy; linear hyperbolic equation",
treatment = "T Theoretical or Mathematical",
}
@Article{DiDonato:1978:AR,
author = "A. R. DiDonato",
title = "An Approximation for $\int^\infty_x e^{-t^2/2} t^p dt,
x > 0, p$ Real",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "271--275",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Naval Surface Weapons Center, Dahlgren, VA, USA",
keywords = "integral approximation; integration; numerical
analysis",
remark = "Fullerton: Closely related to the complementary
incomplete gamma function.",
treatment = "A Application; N New Development; T Theoretical or
Mathematical",
}
@Article{Drezner:1978:CBN,
author = "Z. Drezner",
title = "Computation of the Bivariate Normal Integral",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "277--279",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Faculty of Business, McMaster Univ., Hamilton, Ont.,
Canada",
keywords = "bivariate normal integral; computation; Gauss
quadrature method; integration; numerical analysis",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Dzjadyk:1978:CRP,
author = "V. K. Dzjadyk and L. \=I. F{\'\i}lozof",
title = "The convergence rate of {Pad{\'e}} approximants for
some elementary functions. ({Russian})",
journal = "Mat. Sb. (N.S.)",
volume = "107(149)",
number = "3",
pages = "347--363, 463",
year = "1978",
ISSN = "0368-8666",
MRclass = "41A21 (30E10 41A25)",
MRnumber = "81b:41043",
MRreviewer = "B. D. Donevski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ercegovac:1978:LSR,
author = "Milo{\v{s}} D. Ercegovac",
title = "An On-Line Square Rooting Algorithm",
crossref = "IEEE:1978:PSC",
pages = "183--189",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
abstract = "An on-line algorithm for computing square roots in a
radix 2, normalized floating-point number system with
the redundant digit set $\{-1, 0, 1\}$ is described.
The algorithm has on-line delay of one and it is
amenable for modular implementation. A systematic
approach, used in deriving this algorithm, is presented
in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Book{Feinsilver:1978:SFP,
author = "Philip J. (Philip Joel) Feinsilver",
title = "Special functions, probability semigroups, and
{Hamiltonian} flows",
volume = "696",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 112",
year = "1978",
ISBN = "0-387-09100-9",
ISBN-13 = "978-0-387-09100-6",
LCCN = "QA3 .L28 no. 696; QA273",
bibdate = "Sat Oct 30 19:22:05 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture notes in mathematics",
acknowledgement = ack-nhfb,
subject = "probabilities; semigroups; functions, special;
Hamiltonian systems",
}
@InProceedings{Frankowski:1978:RME,
author = "Krzysztof S. Frankowski",
title = "A Realistic Model for Error Estimates in the
Evaluation of Elementary Functions",
crossref = "IEEE:1978:PSC",
pages = "70--74",
year = "1978",
MRclass = "65G05 (65D20)",
MRnumber = "80g:65050",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1978:CMB,
author = "Walter Gautschi and Josef Slavik",
title = "On the computation of modified {Bessel} function
ratios",
journal = j-MATH-COMPUT,
volume = "32",
number = "143",
pages = "865--875",
month = jul,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4130 (Interpolation
and function approximation)",
corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
USA",
keywords = "Bessel; Bessel functions; continued fraction;
fraction; function approximation; functions; Gauss'
continued; modified Bessel function ratios; Perron's
continued fraction",
treatment = "T Theoretical or Mathematical",
}
@Article{Gustafson:1978:ATC,
author = "S.-\AA. Gustafson",
title = "Algorithm $38$. {Two} computer codes for convergence
acceleration",
journal = j-COMPUTING,
volume = "21",
number = "1",
pages = "87--91",
year = "1978",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65B10",
MRnumber = "83a:65005",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Australian Nat. Univ., Canberra, ACT, Australia",
classification = "723; C4140",
description = "convergence of numerical methods",
journalabr = "Computing (Vienna/New York)",
keywords = "codes, symbolic; convergence acceleration; power
series sum",
}
@Article{Gustafson:1978:CAG,
author = "S.-\AA. Gustafson",
title = "Convergence acceleration on a general class of power
series",
journal = j-COMPUTING,
volume = "21",
number = "1",
pages = "53--69",
year = "1978",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65B10 (40A05)",
MRnumber = "83m:65005",
MRreviewer = "A. M. Cohen",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Australian Nat. Univ., Canberra, ACT, Australia",
classification = "C4120",
description = "convergence of numerical methods; function
evaluation",
keywords = "algorithms; convergence acceleration; power series",
}
@InProceedings{Hull:1978:DFP,
author = "T. E. Hull",
title = "Desirable Floating-Point Arithmetic and Elementary
Functions for Numerical Computation",
crossref = "IEEE:1978:PSC",
pages = "63--69",
year = "1978",
bibdate = "Thu Sep 01 12:14:34 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Morita:1978:CCE,
author = "T. Morita",
title = "Calculation of the complete elliptic integrals with
complex modulus",
journal = j-NUM-MATH,
volume = "29",
number = "2",
pages = "233--236",
month = jan,
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classification = "C4160 (Numerical integration and differentiation)",
corpsource = "Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ.,
Sendai, Japan",
keywords = "complete elliptic integrals; complex modulus;
integration",
remark = "Fullerton: Addendum to a paper by Morita and
Horiguchi.",
treatment = "T Theoretical or Mathematical",
}
@Article{Pexton:1978:RTT,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Roots of two transcendental equations as functions of
a continuous real parameter",
journal = j-MATH-COMPUT,
volume = "32",
number = "142",
pages = "511--518",
month = apr,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Lawrence Livermore Lab., Univ. of California,
Livermore, CA, USA",
keywords = "continuous real parameter; equations; roots; spherical
Bessel functions; transcendental equations",
treatment = "T Theoretical or Mathematical",
}
@Article{Preston:1978:NAT,
author = "F. S. Preston",
title = "A New Algorithm for the Tangent",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "2",
pages = "167--167",
month = feb,
year = "1978",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1978.1675052",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:26 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052",
abstract = "A new mathematical algorithm has been developed for
the tangent. The form of the equation guarantees that
the error is zero at $0^\circ$, $45^\circ$, and
$90^\circ$ corresponding to tangents of $0$, $1$, and
infinity. With only one constant the error is brought
to zero at two more points and the maximum error is
less than one part in $3000$. By adding a second
constant, the error is reduced to less than one in
$720\,000$. Further terms improve the accuracy
geometrically.",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Schindler:1978:GCG,
author = "Susan Schindler and R. Mirman",
title = "Generation of the {Clebsch-Gordan} coefficients for
{$S_n$}",
journal = j-COMP-PHYS-COMM,
volume = "15",
number = "1--2",
pages = "131--145",
month = sep,
year = "1978",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(78)90087-5",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sun Oct 31 09:20:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
}
@Article{Schmidt:1978:EI,
author = "Paul W. Schmidt",
title = "Evaluation of the Integral $\int^\infty_0
\frac{t^{2\alpha-1} J_\nu(x\sqrt{1 + t^2})}{(1 +
t^2)^{\alpha+\beta-1}} dt$",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "265--269",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
keywords = "cylinder diameter distribution; first kind Bessel
function; integral evaluation; integration; long
circular; neutron scattering data; numerical analysis;
power series expansions; recurrence; relations",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Schoene:1978:RMI,
author = "Andrew Y. Schoene",
title = "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
Function [{S14}]''",
journal = j-TOMS,
volume = "4",
number = "3",
pages = "296--304",
month = sep,
year = "1978",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355791.355803",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Aug 30 00:28:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Fullerton:1972:MIG}.",
acknowledgement = ack-nhfb,
}
@Article{Schonfelder:1978:CEE,
author = "J. L. Schonfelder",
title = "{Chebyshev} expansions for the error and related
functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1232--1240",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Computer Centre, Univ. of Birmingham, Birmingham, UK",
keywords = "approximations; Chebyshev approximation; Chebyshev
expansions; error analysis; error function; mappings;
NAG library",
remark = "Fullerton: Approximations for $\erf(x)$, $\erfc(x)$,
and probability functions $P(x)$, $Q(x)$ with accuracy
down to $10^{-30}$.",
treatment = "T Theoretical or Mathematical",
}
@Article{Skovgaard:1978:RCE,
author = "Ove Skovgaard",
title = "Remark on ``{Algorithm 149: Complete Elliptic Integral
[S21]}''",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "95--95",
month = mar,
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:13 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Merner:1962:AAC}.",
acknowledgement = ack-nhfb,
}
@Article{Slepian:1978:PSW,
author = "D. Slepian",
title = "Prolate Spheroidal Wave Functions, {Fourier} Analysis,
and Uncertainty --- {V}: The Discrete Case",
journal = j-BELL-SYST-TECH-J,
volume = "57",
number = "5",
pages = "1371--1430",
month = may # "--" # jun,
year = "1978",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Temme:1978:UAE,
author = "N. M. Temme",
title = "Uniform asymptotic expansions of confluent
hypergeometric functions",
journal = j-J-INST-MATH-APPL,
volume = "22",
number = "2",
pages = "215--223",
year = "1978",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "33A30",
MRnumber = "80a:33004",
MRreviewer = "F. W. J. Olver",
bibdate = "Fri Apr 5 05:48:27 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
}
@Article{Alt:1979:SRD,
author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = j-COMPUTING,
volume = "21",
number = "3",
pages = "221--232",
month = sep,
year = "1979",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25",
MRnumber = "82m:68081",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Math. \& Information, Univ. of Saarlandes,
Saarbrucken, West Germany",
classification = "723; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journalabr = "Computing (Vienna/New York)",
keywords = "algorithm; computer programming; square rooting",
}
@Article{Ardill:1979:ABF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Accurate {Bessel} functions {$J_n(z)$}, {$Y_n(z)$},
{$H_n^{(1)}(z)$} and {$H_n^{(2)}(z)$} of integer order
and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "17",
number = "3",
pages = "321--336",
month = jun,
year = "1979",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(79)90060-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Description of a program with accuracy
about $10^{-10}$.",
}
@Article{Atkins:1979:FSC,
author = "D. E. Atkins",
title = "{Fourth Symposium on Computer Arithmetic}: crunching
with quality and {LSI}",
journal = j-COMPUTER,
volume = "12",
number = "4",
pages = "94--97",
month = apr,
year = "1979",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Computer arithmetic problems --- faster computation
rates and more efficient representations of real
numbers --- are considered in the paper. Floating-point
arithmetic standardization, novel implementation of
basic arithmetic operators, evaluation of elementary
functions --- these are the main considerations of the
conference review.",
acknowledgement = ack-nhfb,
classification = "722; 723",
journalabr = "Computer",
keywords = "computer arithmetic; computer systems, digital; data
processing --- data description; mathematical
techniques --- digital arithmetic",
}
@Article{Babb:1979:OEC,
author = "Stanley E. {Babb, Jr.} and James W. Cafky",
title = "Operational evaluation of certain infinite {Bessel}
function integrals",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1033--1039",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "44A99",
MRnumber = "80e:44002",
MRreviewer = "L. Arteaga",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations)",
corpsource = "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
OK, USA",
keywords = "Bessel function integral; integration; numerical
methods; Schafheitlin method; trigonometric function;
Weber",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Campbell:1979:BFR,
author = "J. B. Campbell",
title = "{Bessel} functions {$J_\nu(x)$} and {$Y_\nu(x)$} of
real order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "18",
number = "1",
pages = "133--142",
month = sep,
year = "1979",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(79)90030-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465579900304",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Carlson:1979:CEI,
author = "B. C. Carlson",
title = "Computing elliptic integrals by duplication",
journal = j-NUM-MATH,
volume = "33",
number = "1",
pages = "1--16",
month = mar,
year = "1979",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20",
MRnumber = "80h:65008",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Logarithms, arctangents, and elliptic integrals of all
three kinds (including complete integrals) are
evaluated numerically by successive applications of the
duplication theorem. When the convergence is improved
by including a fixed number of terms of Taylor's
series, the error ultimately decreases by a factor of
4096 in each cycle of iteration. Except for Cauchy
principal values there is no separation of cases
according to the values of the variables, and no
serious cancellations occur if the variables are real
and nonnegative. Only rational operations and square
roots are required. An appendix contains a recurrence
relation and two new representations (in terms of
elementary symmetric functions and power sums) for
$R$-polynomials, as well as an upper bound for the
error made in truncating the Taylor series of an
$R$-function.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classification = "C4180 (Integral equations)",
corpsource = "Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA",
keywords = "convergence; duplication theory; elliptic integral;
integration; numerical methods; R-polynomial; Taylor
series",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Cole:1979:EI,
author = "R. J. Cole and C. Pescatore",
title = "Evaluation of the Integral $\int_0^\infty t^n
\exp(-t^2 - x/t) \, dt$",
journal = j-J-COMPUT-PHYS,
volume = "32",
number = "2",
pages = "280--287",
month = aug,
year = "1979",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(79)90135-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:34 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999179901359",
abstract = "The main purpose of this paper is to provide a unified
approach to the treatment of linear recurrence
relations for single or pairs of order statistics.
Suppose such a relation has been proved in the simplest
case when $X_1, \ldots{}, X_n$ are independent variates
having an arbitrary absolutely continuous distribution.
It is pointed out that the same relation continues to
hold when the $X$'s are exchangeable, whether
continuous or not. As has recently become well known,
further generalizations are possible when the $X$'s
have any joint distribution. Attention is also drawn to
a useful nonlinear recurrence relation due to Boncelet
(1987).",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
}
@Article{Conde:1979:Z,
author = "S. Conde and S. L. Kalla",
title = "The $\nu$-zeros of ${J}_{-\nu}(x)$",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "423--426",
month = jan,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20",
MRnumber = "80b:65021",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4170 (Differential equations); C4190 (Other numerical
methods)",
corpsource = "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
Venezuela",
keywords = "Bessel function; boundary value; boundary-value
problems; J/sub -v/(x); partial differential equations;
poles and zeros; problems; transforms; v-zeros",
remark = "Fullerton: With a microfiche supplement.",
treatment = "T Theoretical or Mathematical",
}
@Article{Delic:1979:CSS,
author = "G. Delic",
title = "{Chebyshev} series for the spherical {Bessel} function
$j_l(r)$",
journal = j-COMP-PHYS-COMM,
volume = "18",
number = "1",
pages = "73--86",
month = sep,
year = "1979",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(79)90025-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465579900250",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Einarsson:1979:BEN,
author = "Bo Einarsson",
title = "Bibliography on the evaluation of numerical software",
journal = j-J-COMP-APPL-MATH,
volume = "5",
number = "2",
pages = "145--159",
month = jun,
year = "1979",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0771-050X(79)90011-1",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Thu Oct 28 17:14:49 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This bibliography on the evaluation of numerical
software has been written at the request of the IFIP
Working Group on Numerical Software (IFIP WG 2.5), and
is divided into nine different sections. Within each
section the references are given in alphabetical order
by the first author. The aim of the bibliography is to
be useful in the production and evaluation of good
software for numerical mathematics.",
acknowledgement = ack-nhfb,
tableofcontents = "2. Miscellaneous evaluations \\
3. Linear algebra \\
4. Optimization and nonlinear equations \\
5. Functions \\
6. Quadrature \\
7. Integral equations \\
8. Ordinary differential equations \\
9. Partial differential equations",
}
@Article{elLozy:1979:RAS,
author = "Mohamed el Lozy",
title = "Remark on ``{Algorithm 395: Student's
$t$-Distribution}'' and Remark on ``{Algorithm 396:
Student's Quantiles [S14]}''",
journal = j-TOMS,
volume = "5",
number = "2",
pages = "238--239",
month = jun,
year = "1979",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:16 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The algorithms are corrected for computers
with anomalously small word lengths (e.g., IBM and
Interdata).",
}
@Article{Epstein:1979:STE,
author = "H. I. Epstein and B. F. Caviness",
title = "A structure theorem for the elementary functions and
its application to the identity problem",
journal = j-INT-J-COMPUT-INF-SCI,
volume = "8",
number = "1",
pages = "9--37",
year = "1979",
CODEN = "IJCIAH",
ISSN = "0091-7036",
MRclass = "12H05 (68C05)",
MRnumber = "80k:12032",
MRreviewer = "Michael F. Singer",
bibdate = "Sat Apr 26 12:45:53 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Fettis:1979:AEU,
author = "Henry E. Fettis",
title = "An asymptotic expansion for the upper percentage
points of the $\chi^{2}$-distribution",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1059--1064",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "62E20",
MRnumber = "80h:62014",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation)",
keywords = "approximation theory; asymptotic expansion; upper
percentage point",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Gabutti:1979:HPM,
author = "Bruno Gabutti",
title = "On high precision methods for computing integrals
involving {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1049--1057",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D30",
MRnumber = "80c:65048",
MRreviewer = "K. Jetter",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations); C4240 (Programming and
algorithm theory)",
corpsource = "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
Italy",
keywords = "Bessel function integral; computational complexity;
exponential function integral; integration",
treatment = "T Theoretical or Mathematical",
}
@Article{Gautschi:1979:AIG,
author = "W. Gautschi",
title = "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "482--489",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355853.355864",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Aug 28 00:39:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: FORTRAN routines of adjustable accuracy.",
}
@Article{Gautschi:1979:CPI,
author = "Walter Gautschi",
title = "A Computational Procedure for Incomplete Gamma
Functions",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "466--481",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355853.355863",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Aug 28 00:32:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Algorithms for the incomplete gamma
function, $\gamma(a, x)$, the complementary function,
$\Gamma(a, x)$, and Tricomi's form, $\gamma'(a, x)$,
are given.",
}
@Article{Glasser:1979:NI,
author = "M. L. Glasser",
title = "A Note on the Integral $\int^\infty_0t^{2\alpha-1}(1 +
t^2)^{1-\alpha-\beta} {J}_\nu(x\sqrt{1 + t^2}) dt$",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "792--793",
month = apr,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40",
MRnumber = "80d:33004",
MRreviewer = "T. Erber",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4180 (Integral
equations)",
corpsource = "Math. and Computer Sci. Dept., Clarkson Coll. of
Technol., Potsdam, NY, USA",
keywords = "Bessel functions; hypergeometric series; integral;
integral equations",
treatment = "T Theoretical or Mathematical",
}
@Article{Haavie:1979:GNT,
author = "Tore H{\aa}vie",
title = "Generalized {Neville} type extrapolation schemes",
journal = j-BIT,
volume = "19",
number = "2",
pages = "204--213",
month = jun,
year = "1979",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01930850",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65B05 (65D05 65D30)",
MRnumber = "80f:65005",
MRreviewer = "Siegfried Filippi",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204",
acknowledgement = ack-nhfb,
}
@Article{Johnson:1979:RAF,
author = "Donald B. Johnson and Webb Miller and Brian Minnihan
and Celia Wrathall",
title = "Reducibility Among Floating-Point Graphs",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "739--760",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411",
MRclass = "65G05",
MRnumber = "80i:65045",
bibdate = "Fri Dec 08 11:55:10 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The graph-theoretic models of this paper can be used
to compare the rounding-error behavior of numerical
programs. The models follow the approach, popularized
by Wilkinson, of assuming independent rounding errors
in each arithmetic operation. Models constructed on
this assumption are more tractable than would be the
case under more realistic assumptions. There are
identified two easily tested conditions on programs
which guarantee that error analyses are relatively
insensitive to the particular graph model employed. The
development has the additional benefit of sometimes
providing an elementary proof that one program is
comparable in stability to another. Examples of such
results are given.",
acknowledgement = ack-nhfb,
}
@Article{Leung:1979:AFE,
author = "K. V. Leung and S. S. Ghaderpanah",
title = "An application of the finite element approximation
method to find the complex zeros of the modified
{Bessel} function ${K}_{n}(z)$",
journal = j-MATH-COMPUT,
volume = "33",
number = "148",
pages = "1299--1306",
month = oct,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33-04)",
MRnumber = "80e:65024",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
corpsource = "Dept. of Computer Sci., Concordia Univ., Montreal,
Que., Canada",
keywords = "Bessel function; complex zeros; finite element
analysis; finite element approximation method;
iterative optimisation scheme; modified; poles and
zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Maurone:1979:ABD,
author = "Philip A. Maurone and Alain J. Phares",
title = "On the asymptotic behavior of the derivatives of
{Airy} functions",
journal = j-J-MATH-PHYS,
volume = "20",
number = "11",
pages = "2191--2191",
month = nov,
year = "1979",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.523997",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A60",
MRnumber = "80j:33014",
bibdate = "Sat Oct 29 11:28:40 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1",
acknowledgement = ack-nhfb,
classification = "A0230 (Function theory, analysis); A0365D
(Functional analytical methods in quantum theory);
A1235 (Composite models of particles)",
corpsource = "Dept. of Phys., Villanova Univ., Villanova, PA, USA",
keywords = "Airy functions; angular momentum theory; asymptotic
behavior; derivatives; functional analysis;
noniterative functional solution; quantum theory; quark
confinement; recursion relation",
onlinedate = "29 July 2008",
pagecount = "1",
treatment = "T Theoretical or Mathematical",
}
@Article{Morris:1979:DFR,
author = "Robert Morris",
title = "The Dilogarithm Function of a Real Argument",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "778--787",
month = apr,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33A70)",
MRnumber = "80e:65025",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4240 (Programming and algorithm theory)",
corpsource = "Bell Labs., Murray Hill, NJ, USA",
keywords = "algorithm theory; dilogarithm function; real
argument",
remark = "Fullerton: Relative errors down to $10^{-24}$ for
$\operatorname{Li}_2(z) = -\int_0^z \frac{\log(1 -
z)}{z} \, dz$. $\operatorname{Li}_2(z)$ is a form of
Spence's integral.",
treatment = "T Theoretical or Mathematical",
}
@Article{Pexton:1979:DRT,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Degenerate roots of three transcendental equations
involving spherical {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1041--1048",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "loose microfiche suppl. 65H10 (65D20)",
MRnumber = "80g:65057",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Lawrence Livermore Lab., Univ. of California,
Livermore, CA, USA",
keywords = "function approximation; spherical Bessel function;
transcendental equation",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Phillips:1979:FAC,
author = "G. Phillips",
title = "A fast approximation to the complementary error
function for use in fitting gamma-ray peaks",
journal = j-NUCL-INSTR-METH,
volume = "164",
number = "??",
pages = "561--563",
month = sep,
year = "1979",
CODEN = "NUIMAL",
DOI = "http://dx.doi.org/10.1016/0029-554X(79)90094-6",
ISSN = "0029-554X",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
abstract = "A fast approximation to the complementary error
function has been programmed and tested for use in the
peak-shape function for fitting peaks in gamma-ray
spectra. The function was compared for speed and
accuracy on the NRL ASC 7 computer to the mathematical
library version of the complementary error function.
The approximation has resulted in a 50\% time savings
in the computer program HYPERMET which was developed at
NRL for automatic analysis of gamma-ray spectra from
germanium detectors.",
acknowledgement = ack-nhfb,
}
@Article{Risch:1979:APE,
author = "Robert H. Risch",
title = "Algebraic properties of the elementary functions of
analysis",
journal = j-AM-J-MATH,
volume = "101",
number = "4",
pages = "743--759",
year = "1979",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
MRclass = "12H05",
MRnumber = "81b:12029",
MRreviewer = "J. L. Johnson",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Schulten:1979:AEC,
author = "Z. (or K. ??) Schulten and D. G. M. Anderson and R. G.
Gordon",
title = "An Algorithm for the Evaluation of the Complex {Airy}
Functions",
journal = j-J-COMPUT-PHYS,
volume = "31",
number = "1",
pages = "60--75",
month = apr,
year = "1979",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(79)90062-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 10:34:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
remark = "Fullerton: Simple formulae over the whole complex
plane are presented.",
}
@Article{Smith:1979:ALL,
author = "David A. Smith and William F. Ford",
title = "Acceleration of Linear and Logarithmic Convergence",
journal = j-SIAM-J-NUMER-ANAL,
volume = "16",
number = "2",
pages = "223--240",
month = apr,
year = "1979",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B10",
MRnumber = "82a:65012",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
}
@Article{Takemasa:1979:CFC,
author = "T. Takemasa and T. Tamura and H. H. Wolter",
title = "{Coulomb} Functions with Complex Angular Momenta",
journal = j-COMP-PHYS-COMM,
volume = "17",
number = "4",
pages = "351--355",
month = jul # "\slash " # aug,
year = "1979",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(79)90097-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 11:14:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Description of program CCOULOM, which works
only in the part of the $(\rho, \eta)$-plane where
$\eta^2 \ll \rho$ and $|\ell|^2 \ll \rho$.",
}
@Article{Temme:1979:AAP,
author = "N. M. Temme",
title = "An Algorithm with {ALGOL 60} Program for the
Computation of the Zeros of Ordinary {Bessel} Functions
and those of their Derivatives",
journal = j-J-COMPUT-PHYS,
volume = "32",
number = "2",
pages = "270--279",
month = aug,
year = "1979",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(79)90134-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 11:23:13 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
remark = "Fullerton: An adjustable-accuracy 100 line Algol
procedure is discussed.",
}
@Article{Terras:1979:DIG,
author = "Riho Terras",
title = "The determination of incomplete gamma functions
through analytic integration",
journal = j-J-COMPUT-PHYS,
volume = "31",
number = "1",
pages = "146--151",
month = apr,
year = "1979",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(79)90066-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:33 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999179900664",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Thacher:1979:NBR,
author = "Henry C. {Thacher, Jr.}",
title = "New Backward Recurrences for {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "744--764",
month = apr,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33A40)",
MRnumber = "81b:65019",
MRreviewer = "R. G. Langebartel",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
KY, USA",
keywords = "backward recurrences; Bessel functions; converges",
treatment = "N New Development; T Theoretical or Mathematical",
}
@Article{Brent:1980:SNA,
author = "Richard P. Brent and Edwin M. McMillan",
title = "Some new algorithms for high-precision computation of
{Euler}'s constant",
journal = j-MATH-COMPUT,
volume = "34",
number = "149",
pages = "305--312",
month = jan,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "10-04 (10A40 68C05)",
MRnumber = "82g:10002",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Univ. of California, Berkeley, CA, USA",
keywords = "Bessel functions; computation; Euler's constant;
function evaluation; high precision",
remark = "Fullerton: Calculation to 30,100 places is discussed,
but only a 3-digit value appears in the paper.",
treatment = "N New Development; T Theoretical or Mathematical",
}
@InProceedings{Brent:1980:UAE,
author = "R. P. Brent",
title = "Unrestricted Algorithms for Elementary and Special
Functions",
crossref = "Lavington:1980:IPP",
pages = "613--619",
year = "1980",
bibdate = "Thu Sep 01 11:55:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Brezinski:1980:GEA,
author = "C. Brezinski",
title = "A general extrapolation algorithm",
journal = j-NUM-MATH,
volume = "35",
number = "2",
pages = "175--187",
month = jun,
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
MRclass = "65B05",
MRnumber = "81j:65015",
MRreviewer = "L. Fox",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation)",
corpsource = "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
France",
fjournal = "Numerische Mathematik",
keywords = "convergence acceleration; extrapolation; extrapolation
algorithm; linear extrapolation; rational
extrapolation; recursive algorithm; sequence
transformations",
treatment = "T Theoretical or Mathematical",
}
@Article{Char:1980:SCF,
author = "Bruce W. Char",
title = "On {Stieltjes}' continued fraction for the gamma
function",
journal = j-MATH-COMPUT,
volume = "34",
number = "150",
pages = "547--551",
month = apr,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (65D20)",
MRnumber = "81b:65008",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: The first 41 coefficients to 40 digits are
given.",
}
@Book{Cody:1980:SME,
author = "W. J. Cody and W. Waite",
title = "Software Manual for the Elementary Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0-13-822064-6",
ISBN-13 = "978-0-13-822064-8",
LCCN = "QA331 .C635 1980",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Coleman:1980:FSB,
author = "J. P. Coleman",
title = "A {Fortran} subroutine for the {Bessel} function
{$J_n(x)$} of order $0$ to $10$",
journal = j-COMP-PHYS-COMM,
volume = "21",
number = "1",
pages = "109--118",
day = "1",
month = dec,
year = "1980",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(80)90080-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:19 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fortran1.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465580900806",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Delahaye:1980:RNA,
author = "J. P. Delahaye and B. Germain-Bonne",
title = "{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration
de la convergence. ({French}) [{Negative} results in
convergence acceleration]",
journal = j-NUM-MATH,
volume = "35",
number = "4",
pages = "443--457",
month = nov,
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
MRclass = "65B99 (40A99)",
MRnumber = "81k:65007",
MRreviewer = "Claude Brezinski",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
corpsource = "Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq,
France",
keywords = "acceleration; algorithm; approximation theory;
computational complexity; convergence; convergence
acceleration; convergence of numerical methods",
language = "French",
treatment = "T Theoretical or Mathematical",
}
@Article{Ditkin:1980:CSF,
author = "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
title = "The computation of special functions",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "20",
number = "5",
pages = "3--12",
year = "1980",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.2.1; G.1.2",
CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Generating functions; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "algorithms; design",
guideno = "09092",
journalabr = "USSR Comput. Math. Math. Phys",
jrldate = "1980",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Eckhardt:1980:AWE,
author = "Ulrich Eckhardt",
title = "{Algorithm 549}: {Weierstrass}' Elliptic Functions
[{S21}]",
journal = j-TOMS,
volume = "6",
number = "1",
pages = "112--120",
month = mar,
year = "1980",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355873.355884",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Aug 29 10:31:24 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Weierstrass' elliptic functions",
remark = "Fullerton: A complex FORTRAN algorithm with accuracy
down to $10^{-18}$ is given",
}
@Article{Fransen:1980:HPV,
author = "Arne Frans{\'e}n and Staffan Wrigge",
title = "High-precision values of the gamma function and of
some related coefficients",
journal = j-MATH-COMPUT,
volume = "34",
number = "150",
pages = "553--566",
month = apr,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (65D20)",
MRnumber = "81f:65004",
MRreviewer = "F. W. J. Olver",
bibdate = "Sat Apr 01 10:12:58 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See addendum and corrigendum
\cite{Fransen:1981:ACH}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 80D values of coefficients in the Taylor
series for $\Gamma^m(s + x)$ are given.",
}
@TechReport{Fullerton:1980:BEM,
author = "L. W. Fullerton",
title = "A Bibliography on the Evaluation of Mathematical
Functions",
type = "Technical report",
number = "TM 80-1274-4 and CSTR 86",
institution = "Bell Telephone Laboratories",
address = "Murray Hill, NJ, USA",
month = sep,
year = "1980",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Unpublished{Kahan:1980:SPI,
author = "W. Kahan",
title = "Software {$\sqrt{x}$} for the Proposed {IEEE}
Floating-Point Standard",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "????",
day = "25",
month = aug,
year = "1980",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
mynote = "Dated August 25 1980",
}
@Article{Kasperkovitz:1980:AAM,
author = "P. Kasperkovitz",
title = "Asymptotic approximations for modified {Bessel}
functions",
journal = j-J-MATH-PHYS,
volume = "21",
number = "1",
pages = "6--13",
month = jan,
year = "1980",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.524310",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A40",
MRnumber = "81a:33012",
MRreviewer = "N. Hayek Calil",
bibdate = "Sat Oct 29 18:18:22 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1",
acknowledgement = ack-nhfb,
onlinedate = "21 July 2008",
pagecount = "8",
}
@Article{Langebartel:1980:FER,
author = "R. G. Langebartel",
title = "{Fourier} expansions of rational fractions of elliptic
integrals and {Jacobian} elliptic functions",
journal = j-SIAM-J-MATH-ANA,
volume = "11",
number = "3",
pages = "506--513",
month = may,
year = "1980",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "42A16 (33A25)",
MRnumber = "81e:42008",
MRreviewer = "R. C. Varma",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Maksymiv:1980:APT,
author = "E. M. Maksymiv",
booktitle = "Differentsialnye Uravneniya i ikh Prilozhen",
title = "Approximate properties of {Thiele}'s formula in a
class of elementary functions. ({Russian})",
volume = "141",
publisher = "Vestnik L'vov. Politekhn. Inst.",
address = "L'vov, USSR",
pages = "55--56",
year = "1980",
MRclass = "119.65D20",
MRnumber = "81i:65021",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{OBrien:1980:SBF,
author = "D. M. O'Brien",
title = "Spherical {Bessel} functions of large order",
journal = j-J-COMPUT-PHYS,
volume = "36",
number = "1",
pages = "128--132",
month = jun,
year = "1980",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(80)90177-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:01 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999180901771",
abstract = "This note introduces functions $b_n(x)$, related to
spherical Bessel functions $j_n(x)$ and $y_n(x)$. They
are scaled so that they are bounded functions of $n$
and polynomially bounded functions of $x$, and
therefore avoid the problems of underflow and overflow
which are so common with Bessel functions. They can be
generated from a stable recurrence relation for which
starting values are readily computable.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@InProceedings{Olver:1980:UAG,
author = "F. W. J. Olver",
title = "Unrestricted algorithms for generating elementary
functions",
crossref = "Alefeld:1980:PSE",
pages = "131--140",
year = "1980",
MRclass = "65G05 (65D15)",
MRnumber = "82b:65034",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pedersen:1980:HBM,
author = "P. W. Pedersen",
title = "Hvordan beregner man kvadratroden? \toenglish {How do
you calculate the square root?} \endtoenglish",
journal = "Elektronik (Denmark)",
volume = "??",
number = "4",
pages = "18--21",
month = apr,
year = "1980",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Rengarajan:1980:MFI,
author = "S. R. Rengarajan and J. E. Lewis.",
title = "{Mathieu} Functions of Integral Order and Real
Arguments,",
journal = j-IEEE-TRANS-MICROWAVE-THEORY-TECH,
volume = "28",
number = "3",
pages = "276--277",
month = mar,
year = "1980",
CODEN = "IETMAB",
DOI = "http://dx.doi.org/10.1109/TMTT.1980.1130060",
ISSN = "0018-9480",
bibdate = "Sat Oct 30 10:09:01 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "To compute Mathieu functions, modified Mathieu
functions and related parameters for integral orders
and real arguments, encountered in wave propagation
involving elliptic geometries.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: A long FORTRAN program is very briefly
described. This work is superior to that of Clemm
(1969), because $q$ may be negative.",
}
@Article{Schonfelder:1980:VHA,
author = "J. L. Schonfelder",
title = "Very high accuracy {Chebyshev} expansions for the
basic trigonometric functions",
journal = j-MATH-COMPUT,
volume = "34",
number = "149",
pages = "237--244",
month = jan,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20",
MRnumber = "81f:65016",
MRreviewer = "Claude Carasso",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 40D coefficients for the sine, cosine and
tangent are given.",
}
@Book{Sneddon:1980:SFM,
author = "Ian Naismith Sneddon",
title = "Special functions of mathematical physics and
chemistry",
publisher = "Longman",
address = "London, UK",
edition = "Third",
pages = "ix + 182",
year = "1980",
ISBN = "0-582-44396-2 (paperback)",
ISBN-13 = "978-0-582-44396-9 (paperback)",
LCCN = "QA351 .S64 1980",
bibdate = "Sat Oct 30 18:25:01 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Longman mathematical texts",
acknowledgement = ack-nhfb,
remark = "See first edition \cite{Sneddon:1956:SFM} and second
edition \cite{Sneddon:1961:SFM}.",
subject = "Functions, Special",
}
@InCollection{Tretjakov:1980:PSE,
author = "V. A. Tret'jakov",
booktitle = "Mathematical analysis and the theory of functions
({Russian}),",
title = "On the properties of some elementary functions that
are defined on the algebra of bicomplex numbers.
({Russian})",
publisher = "Moskov. Oblast. Ped. Inst.,",
address = "Moscow, USSR",
pages = "99--106",
year = "1980",
MRclass = "30G35 (78A35)",
MRnumber = "82i:30069",
MRreviewer = "Toma V. Tonev",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{vonGudenberg:1980:EAR,
author = "J. Wolff {von Gudenberg}",
title = "{Einbettung allgemeiner Rechnerarithmetik in Pascal
mittels eines Operatorkonzepts und Implementierung der
Standardfunktionen mit optimaler Genauigkeit}
\toenglish {Embedding a General Computer Arithmetic in
Pascal by Means of an Operator Concept and the
Implementation of Elementary Functions with Optimal
Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1980",
bibdate = "Sun Oct 25 10:29:29 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Waldecker:1980:NSR,
author = "D. E. Waldecker",
title = "Nonrestoring Square Root with Simplified Answer
Generation",
journal = j-IBM-TDB,
volume = "22",
number = "11",
pages = "4807--4808",
month = apr,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Bice:1981:AAS,
author = "P. K. Bice",
title = "Algorithm adds square root to micro's arithmetic
capability",
journal = j-ELECTRONIC-DESIGN,
volume = "29",
number = "11",
pages = "146",
month = may,
year = "1981",
CODEN = "ELODAW",
ISSN = "0013-4872",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Branrers:1981:RAZ,
author = "M. Branrers and R. Piessens and M. {De Meue}",
title = "Rational approximations for zeros of {Bessel}
functions",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "403--405",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90253-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902539",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Campbell:1981:BFR,
author = "J. B. Campbell",
title = "{Bessel} functions {$I_\nu(z)$} and {$K_\nu(z)$} of
real order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "24",
number = "1",
pages = "97--105",
month = sep # "\slash " # oct,
year = "1981",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(81)90109-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:27:59 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465581901090",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Carlson:1981:AAI,
author = "B. C. Carlson and Elaine M. Notis",
title = "{Algorithm 577}: Algorithms for Incomplete Elliptic
Integrals [{S21}]",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "398--403",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355958.355970",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Aug 29 22:58:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "$R$-functions; elliptic integrals; inverse circular
functions; inverse hyperbolic functions; logarithms",
}
@Article{Chen:1981:AFD,
author = "Gang Chen",
title = "An attempt to find the derivatives of elementary
functions using the algorithmic language {BCY}.
({Chinese})",
journal = "Zhejiang Daxue Xuebao",
volume = "3",
pages = "141--149",
year = "1981",
MRclass = "26A09",
MRnumber = "714 524",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Davis:1981:EFA,
author = "Diane F. Davis",
title = "Elementary Functions on an Array Processor",
crossref = "IEEE:1981:PIS",
pages = "170--178",
year = "1981",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Delahaye:1981:ACS,
author = "J.-P. Delahaye",
title = "Acc{\'e}l{\'e}ration de la convergence des suites dont
le rapport des erreurs est born{\'e}. ({French})
[{Convergence} acceleration for sequences with bounded
error ratios]",
journal = j-CALCOLO,
volume = "18",
number = "2",
pages = "1--116",
year = "1981",
CODEN = "CDABAE",
DOI = "http://dx.doi.org/10.1007/BF02576491",
ISSN = "0008-0624",
ISSN-L = "0008-0624",
MRclass = "65B05",
MRnumber = "647821 (83a:65004)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Calcolo",
keywords = "convergence acceleration",
language = "{French}",
}
@InProceedings{Farmwald:1981:HBE,
author = "P. Michael Farmwald",
title = "High Bandwidth Evaluation of Elementary Functions",
crossref = "IEEE:1981:PIS",
pages = "139--142",
year = "1981",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Fettis:1981:TEHb,
author = "Henry E. Fettis",
title = "Table errata: {{\em Handbook of elliptic integrals for
engineers and physicists} [second edition, Springer,
New York, 1971 and MR {\bf 43} \#3506] by P. F. Byrd
and M. D. Friedman}",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "317--317",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05",
MRnumber = "82a:65008a",
bibdate = "Sat Apr 12 15:32:35 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Fettis:1981:TETb,
author = "Henry E. Fettis",
title = "Table errata: {{\em A table of the complete elliptic
integral of the first kind for complex values of the
modulus, Part I} [Rep. No. ARL 69-0172, Aerospace Res.
Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR
{\bf 40} \#6725] by Fettis and J. C. Caslin}",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "318",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "318.65A05",
MRnumber = "82a:65010",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Fransen:1981:ACH,
author = "Arne Frans{\'e}n",
title = "Addendum and corrigendum to: {``High-precision values
of the gamma function and of some related
coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150,
553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}",
journal = j-MATH-COMPUT,
volume = "37",
number = "155",
pages = "233--235",
month = jul,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (65D20)",
MRnumber = "82m:65002",
bibdate = "Sat Apr 01 10:12:58 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See \cite{Fransen:1980:HPV}.",
acknowledgement = ack-nhfb,
}
@Article{Fredette:1981:RES,
author = "G. Fredette",
title = "68000 routine extracts square roots",
journal = j-EDN,
volume = "26",
number = "16",
pages = "185--194",
month = aug,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Fullerton:1981:FUMa,
author = "L. W. Fullerton",
title = "{FNLIB} User's Manual Explanatory Table of Contents",
type = "Technical report",
number = "CSTR 92",
institution = "Bell Telephone Laboratories",
address = "Murray Hill, NJ, USA",
month = mar,
year = "1981",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fullerton:1981:FUMb,
author = "L. W. Fullerton",
title = "{FNLIB} User's Manual",
type = "Technical report",
number = "CSTR 95",
institution = "Bell Telephone Laboratories",
address = "Murray Hill, NJ, USA",
month = mar,
year = "1981",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gasper:1981:SFB,
author = "George Gasper",
title = "Summation Formulas for Basic Hypergeometric Series",
journal = j-SIAM-J-MATH-ANA,
volume = "12",
number = "2",
pages = "196--200",
month = mar,
year = "1981",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "82a:33005",
MRreviewer = "L. J. Slater",
bibdate = "Sun Nov 28 19:22:39 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/12/2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Glasser:1981:CBS,
author = "M. L. Glasser",
title = "A Class of {Bessel} Summations",
journal = j-MATH-COMPUT,
volume = "37",
number = "156",
pages = "499--501",
month = oct,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40 (42A16 44A15)",
MRnumber = "82j:33015",
MRreviewer = "B. D. Agrawal",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math. and Computer Sci., Clarkson Coll.,
Potsdam, NY, USA",
keywords = "Bessel functions; Bessel summations; infinite series",
treatment = "T Theoretical or Mathematical",
}
@Article{Haavie:1981:RUT,
author = "Tore H{\aa}vie",
title = "Remarks on a unified theory for classical and
generalized interpolation and extrapolation",
journal = j-BIT,
volume = "21",
number = "4",
pages = "465--474",
month = dec,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01932843",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "41A05 (65D05)",
MRnumber = "83d:41004",
MRreviewer = "G. M{\"u}hlbach",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=465",
acknowledgement = ack-nhfb,
}
@Article{Hill:1981:RSD,
author = "G. W. Hill",
title = "Remark on ``{Algorithm 395: Student's
$t$-Distribution}''",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "247--249",
month = jun,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:18 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
}
@Article{Hill:1981:RSQ,
author = "G. W. Hill",
title = "Remark on ``{Algorithm 396: Student's
$t$-Quantiles}''",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "250--251",
month = jun,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:19 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1970:AASb}.",
acknowledgement = ack-nhfb,
}
@Article{Hough:1981:API,
author = "D. Hough",
title = "Application of the proposed {IEEE 754} standard for
floating-point arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "70--74",
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "Various features of the proposed standard provide an
especially convenient environment for programming
numerical procedures such as the familiar elementary
functions.",
bydate = "MB",
byrev = "Le",
country = "USA",
date = "14/06/82",
descriptors = "Computer arithmetic; floating point; computation
structure; method; application; standard;",
enum = "1418",
language = "English",
location = "RWTH-AC-DFV: Bibl.",
references = "10",
revision = "21/04/91",
}
@Article{James:1981:LTS,
author = "D. G. James",
title = "Linear transformations of the second elementary
function",
journal = j-LIN-MULT-ALGEBRA,
volume = "10",
number = "4",
pages = "347--349",
year = "1981",
CODEN = "LNMLAZ",
ISSN = "0308-1087",
MRclass = "15A69 (10C15)",
MRnumber = "83c:15023",
MRreviewer = "E. W. Ellers",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kunz:1981:QZ,
author = "W. Kunz",
title = "{Quadratwurzel mit dem {$\mu$P Z80}} \toenglish
{Square Roots with the {Z80} Microprocessor}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "7",
pages = "109--110",
year = "1981",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Longman:1981:DCA,
author = "I. M. Longman",
booktitle = "{Pad{\'e} approximation and its applications,
Amsterdam 1980 (Amsterdam, 1980)}",
title = "Difficulties of convergence acceleration",
volume = "888",
publisher = pub-SV,
address = pub-SV:adr,
pages = "273--289",
year = "1981",
MRclass = "65B10",
MRnumber = "649102 (83d:65013)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Maino:1981:CPC,
author = "G. Maino and E. Menapace and A. Ventura",
title = "Computation of parabolic cylinder functions by means
of a {Tricomi} expansion",
journal = j-J-COMPUT-PHYS,
volume = "40",
number = "2",
pages = "294--304",
month = apr,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90211-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:06 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902114",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Markov:1981:ICE,
author = "S. M. Markov",
title = "On the interval computation of elementary functions",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "34",
number = "3",
pages = "319--322",
year = "1981",
CODEN = "DBANAD",
ISSN = "0366-8681",
MRclass = "65G10",
MRnumber = "83e:65084",
MRreviewer = "David F. Griffiths",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{McCullagh:1981:RCS,
author = "Peter McCullagh",
title = "A rapidly convergent series for computing $\psi (z)$
and its derivatives",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "247--248",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33A15)",
MRnumber = "81m:65028",
MRreviewer = "J. Gregor",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007741",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Imperial Coll. of Sci. and Technol., London, UK",
keywords = "(mathematics); convergence; function evaluation; log
gamma function; poles; poles and zeros; rapidly
convergent series; series; series expansion; uniformly
convergent",
treatment = "T Theoretical or Mathematical",
}
@Article{Moon:1981:AFC,
author = "Wooil Moon",
title = "{Airy} function with complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "22",
number = "4",
pages = "411--417",
month = may,
year = "1981",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 09:27:06 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465581901387",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@InProceedings{Peng:1981:AES,
author = "Hong Peng",
title = "Algorithms for extracting square roots and cube
roots",
crossref = "IEEE:1981:PSC",
pages = "121--126",
year = "1981",
bibdate = "Thu Sep 01 11:37:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
abstract = "This paper describes a kind of algorithms for fast
extracting square roots and cube roots, their
mathematical proofs, their revised algorithm formulae,
and hardware implementation of the square root
algorithm. These algorithms may be of no significance
for large scale computer with fast division. But I am
sure that it is effective and economical to apply these
algorithms to the circuit designs of some mini- and
microcomputers with general multiplication and
division, such as nonrestoring division.",
acknowledgement = ack-nj,
keywords = "ARITH-5",
}
@Article{Razaz:1981:RAF,
author = "M. Razaz and J. L. Schonfelder",
title = "Remark on ``{Algorithm} 498: {Airy} Functions Using
{Chebyshev} Series Approximations''",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "404--405",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/355958.355971",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Aug 30 00:28:07 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Prince:1975:AAF}.",
acknowledgement = ack-nhfb,
}
@Article{Schulten:1981:NAE,
author = "Z. Schulten and R. G. Gordon and D. G. M. Anderson",
title = "A numerical algorithm for the evaluation of {Weber}
parabolic cylinder functions {$U(a, x)$}, {$V(a, x)$},
and {$W(a, \pm x)$}",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "213--237",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90241-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902412",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Smith:1981:ERA,
author = "J. M. Smith and F. W. J. Olver and D. W. Lozier",
title = "Extended-Range Arithmetic and Normalized {Legendre}
Polynomials",
journal = j-TOMS,
volume = "7",
number = "1",
pages = "93--105",
month = mar,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20 (65G05)",
MRnumber = "83a:65017",
bibdate = "Mon Aug 29 22:02:12 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/355934.355940",
acknowledgement = ack-nhfb,
keywords = "angular momentum; extended-range arithmetic; Legendre
polynomials; overflow; underflow",
}
@Article{Steinberg:1981:LSE,
author = "D. Steinberg and M. Rodeh",
title = "A layout for the shuffle-exchange network with
{$O(N^2/\log^{3/2}N)$} area",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-30",
number = "12",
pages = "977--982",
month = dec,
year = "1981",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1981.1675738",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "C.1.2; G.1.2",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Interconnection architectures;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Interconnection architectures;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "design",
guideno = "06519",
jrldate = "Dec. 1981",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Steinhardt:1981:ASF,
author = "Paul J. Steinhardt and P. Chaudhari",
title = "{Airy} stress function for atomic models",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "266--276",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90244-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902448",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@InProceedings{Taylor:1981:CHD,
author = "George S. Taylor",
title = "Compatible hardware for division and square root",
crossref = "IEEE:1981:PSC",
pages = "127--134",
year = "1981",
bibdate = "Mon Sep 16 16:30:51 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
abstract = "Hardware for radix four division and radix two square
root is shared in a processor designed to implement the
proposed IEEE floating-point standard. The division
hardware looks ahead to find the next quotient digit in
parallel with the next partial remainder. An 8-bit ALU
estimates the next remainder's leading bits. The
quotient digit look-up table is addressed with a
truncation of the estimate rather than a truncation of
the full partial remainder. The estimation ALU and the
look-up table are asymmetric for positive and negative
remainders. This asymmetry reduces the width of the ALU
and the number of minterms in the logic equations for
the look-up table. The square root algorithm obtains
the correctly rounded result in about two division
times using small extensions to the division
hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Terras:1981:ASI,
author = "Riho Terras",
title = "Algorithms for some integrals of {Bessel} functions
and multivariate {Gaussian} integrals",
journal = j-J-COMPUT-PHYS,
volume = "41",
number = "1",
pages = "192--199",
month = may,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90087-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:06 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181900875",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Terras:1981:MAI,
author = "Riho Terras",
title = "A {Miller} algorithm for an incomplete {Bessel}
function",
journal = j-J-COMPUT-PHYS,
volume = "39",
number = "1",
pages = "233--240",
month = jan,
year = "1981",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(81)90147-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:04 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181901479",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Vogelius:1981:DRM,
author = "M. Vogelius and I. Babuska",
title = "On a dimensional reduction method. {II}. {Some}
approximation-theoretic results",
journal = j-MATH-COMPUT,
volume = "37",
number = "155",
pages = "47--68",
month = jul,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.7 Ordinary Differential Equations;
G.1.7 Boundary value problems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems",
genterm = "theory",
guideno = "09396",
jrldate = "July 1981",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Wimp:1981:STT,
author = "Jet Wimp",
title = "Sequence Transformations and Their Applications",
volume = "154",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 257",
year = "1981",
ISBN = "0-08-095662-9 (e-book), 0-12-757940-0",
ISBN-13 = "978-0-08-095662-6 (e-book), 978-0-12-757940-5",
LCCN = "QA292 .W54",
bibdate = "Thu Dec 1 11:08:47 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering",
URL = "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=453177",
acknowledgement = ack-nhfb,
subject = "Sequences (Mathematics) Transformations (Mathematics)
Numerical analysis; Acceleration of convergence",
tableofcontents = "Front Cover \\
Sequence Transformations and Their Applications \\
Copyright Page \\
Contents \\
Preface \\
Acknowledgments \\
Notation \\
Chapter 1. Sequences and Series \\
Chapter 2. Linear Transformations \\
Chapter 3. Linear Lozenge Methods \\
Chapter 4. Optimal Methods and Methods Based on Power
Series \\
Chapter 5. Nonlinear Lozenges \\
Iteration Sequences \\
Chapter 6. The Schmidt Transformation \\
The e-Algorithm \\
Chapter 7. Aitken's $d^2$-Process and Related Methods
\\
Chapter 8. Lozenge Algorithms and the Theory of
Continued Fractions \\
Chapter 9. Other Lozenge Algorithms and Nonlinear
MethodsChapter 10. The Brezinski--H{\aa}vie
ProtocolChapter 11. The Brezinski--H{\aa}vie Protocol
and Numerical Quadrature \\
Chapter 12. Probabilistic Methods \\
Chapter 13. Multiple Sequences \\
Appendix \\
Bibliography \\
Index",
}
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: {A} $\sqrt(x)$
Comparison",
journal = j-IEEE-MICRO,
volume = "2",
number = "3",
pages = "63--79",
month = may,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.290970",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Colorado State Univ., Fort Collins, CO, USA",
fjournal = "IEEE Micro",
keywords = "16-bit machines; 8-bit machine; accuracy; Chen method;
computer testing; Cordic method; direct method;
function approximation; hardware; Intel 8080; Newton
method; PDP-11/20; software requirements; speed;
square-roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Armengou:1982:ASQ,
author = "Santiago Zarzuela Armengou",
title = "About some questions of differential algebra
concerning to elementary functions",
journal = "Publ. Sec. Mat. Univ. Aut{\`o}noma Barcelona",
volume = "26",
number = "1",
pages = "5--15",
year = "1982",
MRclass = "12H05",
MRnumber = "86i:12009",
MRreviewer = "Michael F. Singer",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Barnett:1982:CCB,
author = "A. R. Barnett",
title = "{COULFG}: {Coulomb} and {Bessel} functions and their
derivatives, for real arguments, by {Steed}'s method",
journal = j-COMP-PHYS-COMM,
volume = "27",
number = "2",
pages = "147--166",
month = aug,
year = "1982",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(82)90070-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:03 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465582900704",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Barnett:1982:CFE,
author = "A. R. Barnett",
title = "Continued-fraction evaluation of {Coulomb} functions
{$F_\lambda(\eta, x)$}, {$G_\lambda(\eta, x)$} and
their derivatives",
journal = j-J-COMPUT-PHYS,
volume = "46",
number = "2",
pages = "171--188",
month = may,
year = "1982",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(82)90012-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:11 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999182900122",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@TechReport{Bazarov:1982:EEF,
author = "M. B. Bazarov and Yu. I. Shokin and Z. Kh. Yuldashev",
title = "On the Evaluation of Elementary Functions in Interval
Analysis (In {Russian})",
institution = "Applied Mathematics and Mechanics, Tashkent State
Univ.",
address = "Tashkent, USSR",
pages = "26--31",
year = "1982",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr # "\slash " # ack-nhfb,
}
@Article{Belevitch:1982:SIT,
author = "V. Belevitch and J. Boersma",
title = "On {Stieltjes} integral transforms involving
{$\Gamma$}-functions",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "223--226",
month = jan,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "44A15 (33A15 33A45)",
MRnumber = "83d:44001",
MRreviewer = "V. M. Bhise",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Philips Res Lab., Brussels, Belgium",
keywords = "Gamma functions; integral transforms; Stieltjes
transforms; systematic classification; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1982:MNT,
author = "P. B. Borwein",
title = "On a method of {Newman} and a theorem of {Bernstein}",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "1",
pages = "37--41",
month = jan,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06012",
jrldate = "Jan. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Brezinski:1982:ASG,
author = "C. Brezinski",
title = "{Algorithm 585}: {A} Subroutine for the General
Interpolation and Extrapolation Problems",
journal = j-TOMS,
volume = "8",
number = "3",
pages = "290--301",
month = sep,
year = "1982",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/356004.356008",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Aug 29 23:49:19 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
keywords = "algorithms; convergence acceleration; extrapolation;
interpolation; least squares approximation;
Neville--Aitken scheme",
}
@Article{Brezinski:1982:SNC,
author = "Claude Brezinski",
title = "Some New Convergence Acceleration Methods",
journal = j-MATH-COMPUT,
volume = "39",
number = "159",
pages = "133--145",
month = jul,
year = "1982",
CODEN = "MCMPAF",
DOI = "http://dx.doi.org/10.2307/2007624",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65B05",
MRnumber = "658218 (83f:65003)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
keywords = "convergence acceleration",
}
@Book{Carroll:1982:TST,
author = "Robert Wayne Carroll",
title = "Transmutation, scattering theory, and special
functions",
volume = "87; 69",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "x + 457",
year = "1982",
ISBN = "0-444-86426-1 (paperback)",
ISBN-13 = "978-0-444-86426-0 (paperback)",
LCCN = "QA1 .N86 no. 87; QA329",
bibdate = "Sat Oct 30 18:29:29 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "North-Holland mathematics studies",
acknowledgement = ack-nhfb,
subject = "Transmutation operators; Scattering (Mathematics);
Inverse problems (Differential equations); Functions,
Special",
}
@Article{Chambers:1982:UBF,
author = "Ll. G. Chambers",
title = "An upper bound for the first zero of {Bessel}
functions",
journal = j-MATH-COMPUT,
volume = "38",
number = "158",
pages = "589--591",
month = apr,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A65",
MRnumber = "83h:33011",
MRreviewer = "S. Ahmed",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@InProceedings{Cody:1982:TTP,
author = "W. J. Cody",
title = "Transportable test procedures for elementary function
software",
crossref = "Mulvey:1982:EMP",
pages = "236--247",
year = "1982",
bibdate = "Thu Nov 17 06:39:08 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
}
@Article{Crick:1982:IRB,
author = "S. E. Crick",
title = "Inclusion relations for {Bernstein} quasi-analytic
classes",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "4",
pages = "375--379",
month = apr,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; theory",
guideno = "07841",
jrldate = "April 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Cruz:1982:ZHF,
author = "Andr{\'e}s Cruz and Javier Sesma",
title = "Zeros of the {Hankel} function of real order and of
its derivative",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "639--645",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40",
MRnumber = "83j:33005",
MRreviewer = "S. Ahmed",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation)",
corpsource = "Dept. de Fisica Teorica, Univ. de Zaragoza, Zaragoza,
Spain",
keywords = "approximation; derivative; evaluation; function
approximation; function evaluation; Hankel function;
poles and zeros; real order; trajectories; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Danielopoulos:1982:CEP,
author = "S. D. Danielopoulos",
title = "On the Cost of Evaluating Polynomials and Their
Derivatives",
journal = j-COMPUTING,
volume = "29",
number = "4",
pages = "373--380",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25 (68C20)",
MRnumber = "84a:68039",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ of Ioannina, Greece",
catcode = "G.1.2; G.4; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Algorithm analysis; G.1.0 General;
G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic",
genterm = "economics; theory",
guideno = "04049",
journalabr = "Computing (Vienna/New York)",
jrldate = "1982",
keywords = "mathematical techniques",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Decker:1982:CAN,
author = "D. W. Decker and C. T. Kelley",
title = "Convergence acceleration for {Newton}'s method at
singular points",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "1",
pages = "219--229",
month = feb,
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
MRclass = "65H05 (58E07 65J15)",
MRnumber = "83e:65090",
MRreviewer = "Michael Pr{\"u}fer",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Delahaye:1982:SLC,
author = "J. P. Delahaye and B. Germain-Bonne",
title = "The set of logarithmically convergent sequences cannot
be accelerated",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "4",
pages = "840--844",
month = aug,
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B99",
MRnumber = "83f:65005",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
keywords = "convergence acceleration",
}
@Article{Epstein:1982:UAF,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {I}: function data types",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "1--18",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.2; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.2
Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms",
guideno = "09324",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Epstein:1982:UAI,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {II}: intervals of polynomials",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "19--29",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.1; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation; G.1.0 General;
G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Error analysis",
genterm = "algorithms",
guideno = "09325",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Fernandez:1982:HCI,
author = "F. M. Fern{\'a}ndez and A. Mes{\'o}n and E. A.
Castro",
title = "Hypervirial calculation of integrals involving
{Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "23",
number = "2",
pages = "254--255",
month = feb,
year = "1982",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.525345",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C05 (33A40 82A51)",
MRnumber = "83c:81010",
bibdate = "Sat Oct 29 18:19:03 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i2/p254_s1",
acknowledgement = ack-nhfb,
pagecount = "2",
}
@Article{Gawronski:1982:ACF,
author = "W. Gawronski and U. Stadtm{\"u}ller",
title = "Approximation of continuous functions by generalized
{Favard} operators",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "4",
pages = "384--396",
month = apr,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory; algorithms",
guideno = "06038",
jrldate = "April 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Gessel:1982:SEH,
author = "Ira Gessel and Dennis Stanton",
title = "Strange Evaluations of Hypergeometric Series",
journal = j-SIAM-J-MATH-ANA,
volume = "13",
number = "2",
pages = "295--308",
month = mar,
year = "1982",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "83c:33002",
MRreviewer = "C. L. Parihar",
bibdate = "Sun Nov 28 19:22:53 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/13/2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Gordon:1982:RAN,
author = "H. T. Gordon",
title = "Rough approximation numerical algorithms",
journal = j-DDJ,
volume = "7",
number = "7",
pages = "54--56",
month = jul,
year = "1982",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1.2",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
guideno = "04547",
jrldate = "July 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Greaves:1982:AHM,
author = "G. Greaves",
title = "An algorithm for the {Hausdorff} moment problem",
journal = j-NUM-MATH,
volume = "39",
number = "2",
pages = "231--238",
month = aug,
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms",
guideno = "07489",
jrldate = "Aug. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Hermann:1982:SAG,
author = "Robert Hermann",
title = "Some algebraic, geometric, and system-theoretic
properties of the {Special Functions} of mathematical
physics",
journal = j-J-MATH-PHYS,
volume = "23",
number = "7",
pages = "1282--1294",
month = jul,
year = "1982",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.525511",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Sat Oct 29 18:19:10 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i7/p1282_s1",
abstract = "It is known that many of the Special Functions of
mathematical physics appear as matrix elements of Lie
group representations. This paper is concerned with a
beginning attack on the converse problem, i.e., finding
conditions that a given function be a matrix element.
The methods used are based on a combination of ideas
from system theory, functional analysis, Lie theory,
differential algebra, and linear ordinary differential
equation theory. A key idea is to attach a symbol as an
element of a commutative algebra. In favorable cases,
this symbol defines a Riemann surface, and a
meromorphic differential form on that surface. The
topological and analytical invariants attached to this
form play a key role in system theory. The Lie algebras
of the groups appear as linear differential operators
on this Riemann surface. Finally, it is shown how the
Picard--Vessiot--Infeld--Hull theory of factorization
of linear differential operators leads to realization
of many Special Functions as matrix representations of
group representations.",
acknowledgement = ack-nhfb,
pagecount = "13",
}
@TechReport{Kahan:1982:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions",
type = "Technical Report",
number = "PAM-105",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
year = "1982",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "na, elementary function",
}
@Article{Keener:1982:CLB,
author = "L. L. Keener",
title = "Characterizing local best {SAIN} approximations",
journal = j-J-APPROX-THEORY,
volume = "36",
number = "1",
pages = "55--63",
month = sep,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Chebyshev approximation and theory;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06074",
jrldate = "Sept. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Lassey:1982:CCI,
author = "Keith R. Lassey",
title = "On the computation of certain integrals containing the
modified {Bessel} function ${I}_{0}(\xi )$",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "625--637",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20",
MRnumber = "83j:65029",
MRreviewer = "Walter Gautschi",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
C4130 (Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Inst. of Nuclear Sci., DSIR, Lower Hutt, New Zealand",
keywords = "approximation; approximation theory; convergence of
numerical methods; convergent series; function;
function approximation; integration; limiting
behaviour; modified Bessel; numerical integration;
one-dimensional integrals; two-dimensional integrals",
treatment = "T Theoretical or Mathematical",
}
@Article{Ling:1982:EIH,
author = "Chih Bing Ling and Ming Jing Wu",
title = "Evaluation of integrals of {Howland} type involving a
{Bessel} function",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "215--222",
month = jan,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (65D20)",
MRnumber = "82m:65003",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); B0290M (Numerical
integration and differentiation); C1120 (Mathematical
analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Maths., Virginia Polytech. Inst. and State
Univ., Blacksburg, VA, USA",
keywords = "10D; 20D; accuracy; Bessel function; Bessel functions;
Howland type; integrals; integration; tabulated
values",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Mori:1982:ARS,
author = "S. Mori and C. Y. Suen",
editor = "Ching Y. Suen and Renato {De Mori}",
key = "Scanners",
booktitle = "Computer analysis and perception: vol. I, {Visual}
signals",
title = "Automatic recognition of symbols and architecture of
the recognition unit",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "17--40",
year = "1982",
ISBN = "0-8493-6305-5 (vol. 1), 0-8493-6306-3 (vol. 2)",
ISBN-13 = "978-0-8493-6305-4 (vol. 1), 978-0-8493-6306-1 (vol.
2)",
LCCN = "TA1650 .C65 1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bookpages = "various",
catcode = "I.5; G.1.2; C.3; B.7; I.5.4",
CRclass = "I.5.2 Design Methodology; G.1.2 Approximation; G.1.2
Elementary function approximation; C.3 Signal
processing systems; B.7.1 Types and Design Styles;
I.5.4 Applications; I.5.4 Signal processing",
descriptor = "Computing Methodologies, PATTERN RECOGNITION, Design
Methodology; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Computer Systems Organization,
SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
processing systems; Hardware, INTEGRATED CIRCUITS,
Types and Design Styles; Computing Methodologies,
PATTERN RECOGNITION, Applications, Signal processing",
genterm = "documentation; theory; design",
guideno = "01691",
subject = "I. Computing Methodologies; I.5 PATTERN RECOGNITION;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C.
Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; B. Hardware; B.7 INTEGRATED
CIRCUITS; I. Computing Methodologies; I.5 PATTERN
RECOGNITION",
}
@Article{Oklobdzija:1982:LSR,
author = "V. G. Oklobdzija and M. D. Ercegovac",
title = "An On-Line Square Root Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "1",
pages = "70--75",
month = jan,
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1675887",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:09 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Ollin:1982:CFE,
author = "H. Z. Ollin and I. Gerst",
title = "Classes of functions with explicit best uniform
approximations",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "3",
pages = "264--276",
month = mar,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06030",
jrldate = "March 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Piessens:1982:ACB,
author = "R. Piessens",
title = "Automatic computation of {Bessel} function integrals",
journal = j-COMP-PHYS-COMM,
volume = "25",
number = "3",
pages = "289--295",
month = mar,
year = "1982",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:01 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465582900248",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Rack:1982:GIV,
author = "H.-J Rack",
title = "A generalization of an inequality of {V. Markov} to
multivariate polynomials",
journal = j-J-APPROX-THEORY,
volume = "35",
number = "1",
pages = "94--97",
month = may,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06047",
jrldate = "May 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Rix:1982:UQA,
author = "P. Rix",
title = "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
\toenglish {Universal Square Root Algorithms}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "23",
pages = "81--82",
year = "1982",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@PhdThesis{Rockey:1982:DMS,
author = "S. A. Rockey",
title = "Discrete methods of state approximation, parameter
identification and optimal control for hereditary
systems",
type = "{Ph.D} Thesis",
school = "Brown University",
address = "Providence, RI",
pages = "208",
year = "1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.2; G.1.5",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Linear
approximation; G.1.5 Roots of Nonlinear Equations;
G.1.5 Convergence",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Convergence",
guideno = "15449",
source = "UMI order no. DA8228325",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Sommer:1982:EPL,
author = "M. Sommer",
title = "Existence of pointwise-{Lipschitz}-continuous
selections of the metric projection for a class of
{$Z$}-spaces",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "2",
pages = "115--130",
month = feb,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06018",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@PhdThesis{Wang:1982:AME,
author = "J.-L Wang",
title = "Asymptotically minimax estimators for distributions
with increasing failure rate",
type = "{Ph.D} Thesis",
school = "University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "42",
year = "1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "design",
guideno = "15084",
source = "UMI order no. DA8300696",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Whitley:1982:MBI,
author = "R. Whitley",
title = "{Markov} and {Bernstein}'s inequalities, and compact
and strictly singular operators",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "3",
pages = "277--285",
month = mar,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "06031",
jrldate = "March 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Wills:1982:RCA,
author = "C. A. Wills and J. M. Blair and P. L. Ragde",
title = "Rational {Chebyshev} approximations for the {Bessel}
functions ${J}_{0}(x)$, ${J}_{1}(x)$, ${Y}_{0}(x)$,
${Y}_{1}(x)$",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "617--623",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33A40 41A50)",
MRnumber = "83j:65030",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0260 (Optimisation techniques); B0290F (Interpolation
and function approximation); C1180 (Optimisation
techniques); C4130 (Interpolation and function
approximation)",
corpsource = "AEG Ltd., Chalk River Nuclear Labs., Ont., Canada",
keywords = "approximations; Bessel functions; Chebyshev; Chebyshev
approximation; formulae; McMahon asymptotic; minimax
techniques; near-minimax rational approximation",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Wimp:1982:CMS,
author = "Jet (Jesse Jet) Wimp",
title = "Computational methods and special functions",
type = "{D.Sc.} thesis",
school = "University of Edinburgh",
address = "Edinburgh, UK",
year = "1982",
bibdate = "Thu Dec 01 11:15:32 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Amos:1983:APF,
author = "Donald E. Amos",
title = "{Algorithm 610}: {A} Portable {FORTRAN} Subroutine for
Derivatives of the Psi Function",
journal = j-TOMS,
volume = "9",
number = "4",
pages = "494--502",
month = dec,
year = "1983",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/356056.356065",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20",
MRnumber = "791 979",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1; G; D.3.2",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.m
Miscellaneous; D.3.2 Language Classifications; D.3.2
FORTRAN",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Miscellaneous; Mathematics of
Computing, MISCELLANEOUS; Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN",
genterm = "ALGORITHMS",
guideno = "02212",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.m MISCELLANEOUS; D.
Software; D.3 PROGRAMMING LANGUAGES",
}
@Article{Benton:1983:CZT,
author = "T. C. Benton",
title = "Common Zeros of Two {Bessel} Functions. {Part II}.
{Approximations} and Tables",
journal = j-MATH-COMPUT,
volume = "41",
number = "163",
pages = "203--217",
month = jul,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40 (65A05)",
MRnumber = "85a:33010",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math., Pennsylvania State Univ., University
Park, PA, USA",
keywords = "Bessel functions; computer program; poles and zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Brezinski:1983:CAE,
author = "C. Brezinski and J. P. Delahaye and B. Germain-Bonne",
title = "Convergence acceleration by extraction of linear
subsequences",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "6",
pages = "1099--1105",
month = dec,
year = "1983",
CODEN = "SJNAAM",
DOI = "http://dx.doi.org/10.1137/0720079",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B99 (40A05)",
MRnumber = "723826 (85g:65014)",
MRreviewer = "John H. McCabe",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
keywords = "convergence acceleration",
}
@Article{Brezinski:1983:ECC,
author = "Claude Brezinski",
title = "Error control in convergence acceleration processes",
journal = j-IMA-J-NUMER-ANAL,
volume = "3",
number = "1",
pages = "65--80",
year = "1983",
CODEN = "IJNADH",
DOI = "http://dx.doi.org/10.1093/imanum/3.1.65",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65B99 (65D32 65G05)",
MRnumber = "705081 (85a:65004)",
MRreviewer = "John P. Coleman",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
keywords = "convergence acceleration",
}
@Article{Cash:1983:BRKa,
author = "J. R. Cash",
title = "Block {Runge--Kutta} Methods for the Numerical
Integration of Initial Value Problems in Ordinary
Differential Equations. {Part I}. {The} Nonstiff Case",
journal = j-MATH-COMPUT,
volume = "40",
number = "161",
pages = "175--191",
month = jan,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65L05",
MRnumber = "84d:65044a",
MRreviewer = "W. C. Rheinboldt",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4160 (Numerical
integration and differentiation); C4170 (Differential
equations)",
corpsource = "Dept. of Math., Imperial Coll., London, UK",
keywords = "approximate numerical integration; approximation
theory; block implicit formulae; block Runge--Kutta
formulae; C. W. Gear; differential equations;
equations; first order; formulae; initial value;
initial value problems; integration; linear multistep
methods; nonstiff problems; order; ordinary
differential; problems; Runge--Kutta methods;
Runge--Kutta starters; stepsize; stiff problems;
systems; variable order; variable order block
explicit",
treatment = "T Theoretical or Mathematical",
}
@Article{Cody:1983:ASM,
author = "W. J. Cody",
title = "Algorithm 597: Sequence of Modified {Bessel} Functions
of the First Kind",
journal = j-TOMS,
volume = "9",
number = "2",
pages = "242--245",
month = jun,
year = "1983",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MISCELLANEOUS",
genterm = "algorithms",
guideno = "02186",
jrldate = "June 1983",
keywords = "algorithms",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation G
Mathematics of Computing, MISCELLANEOUS",
}
@Article{Coleman:1983:CEB,
author = "J. P. Coleman and A. J. Monaghan",
title = "{Chebyshev} expansions for the {Bessel} function
${J}_{n}(z)$ in the complex plane",
journal = j-MATH-COMPUT,
volume = "40",
number = "161",
pages = "343--366",
month = jan,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (30E10 33A40 65D20)",
MRnumber = "84c:65013",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Cruz:1983:MPR,
author = "Andr{\'e}s Cruz and Javier Sesma",
title = "Modulus and phase of the reduced logarithmic
derivative of the {Hankel} function",
journal = j-MATH-COMPUT,
volume = "41",
number = "164",
pages = "597--605",
month = oct,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40 (65H05 81F10)",
MRnumber = "85b:33006",
MRreviewer = "H. E. Fettis",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Demsky:1983:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "3",
pages = "237--244",
month = may,
year = "1983",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:04 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900048",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Dietrich:1983:VQF,
author = "D. Dietrich",
title = "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
Mikrorechnerprozeduren} \toenglish {Methods for the
Solution of Square Roots for Microprocessor
Subroutines} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "EL-1--EL-6",
year = "1983",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Dec 08 13:05:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dubrulle:1983:CNM,
author = "Augustin A. Dubrulle",
title = "Class of Numerical Methods for the Computation of
{Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "582--589",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Moler:1983:RSR} and generalization
\cite{Jamieson:1989:RCI}.",
abstract = "Moler and Morrison have described an iterative
algorithm for the computation of the Pythagorean sum
(a**2 plus b**2)** one-half of two real numbers a and
b. This algorithm is immune to unwarranted
floating-point overflows, has a cubic rate of
convergence, and is easily transportable. This paper,
which shows that the algorithm is essentially Halley's
method applied to the computation of square roots,
provides a generalization to any order of convergence.
Formulas of orders 2 through 9 are illustrated with
numerical examples. The generalization keeps the number
of floating-point divisions constant and should be
particularly useful for computation in high-precision
floating-point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
classification = "723; 921",
corpsource = "IBM Sci. Centre, Palo Alto, CA, USA",
journalabr = "IBM J Res Dev",
keywords = "computer programming; digital arithmetic;
floating-point divisions; Halley's method;
high-precision floating-point arithmetic; iterative
algorithm; iterative methods; mathematical techniques
--- Numerical Methods; Pythagorean sums; rate of
convergence; square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Ellacott:1983:FTE,
author = "S. W. Ellacott",
title = "On the {Faber} transform and efficient numerical
rational approximation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "5",
pages = "989--1000",
month = oct,
year = "1983",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "41A20 (41A21)",
MRnumber = "85f:41010",
MRreviewer = "Lee L. Keener",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Fessler:1983:HAA,
author = "Theodore Fessler and William F. Ford and David A.
Smith",
title = "{HURRY}: An Acceleration Algorithm for Scalar
Sequences and Series",
journal = j-TOMS,
volume = "9",
number = "3",
pages = "346--354",
month = sep,
year = "1983",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/356044.356051",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65B10",
MRnumber = "791 970",
bibdate = "Sun Sep 04 19:50:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
}
@Article{Fukushima:1983:OAA,
author = "M. Fukushima",
title = "An outer approximation algorithm for solving general
convex programs",
journal = j-OPER-RES,
volume = "31",
number = "1",
pages = "101--113",
month = feb,
year = "1983",
CODEN = "OPREAI",
ISSN = "0030-364X (print), 1526-5463 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.4",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency",
genterm = "algorithms; documentation; performance; reliability;
theory",
guideno = "09992",
jrldate = "Jan./Feb. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE",
}
@Article{Giordano:1983:EAZ,
author = "C. Giordano and A. Laforgia",
title = "Elementary approximations for zeros of {Bessel}
functions",
journal = j-J-COMP-APPL-MATH,
volume = "9",
number = "3",
pages = "221--228",
month = sep,
year = "1983",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "08115",
jrldate = "Sept. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Hasson:1983:C,
author = "M. Hasson and O. Shisha",
title = "On the condition
$\sum^{\infty}_{n=1}n^{p-1}{E}^{*}_{n}(f) < \infty$",
journal = j-J-APPROX-THEORY,
volume = "39",
number = "4",
pages = "389--398",
month = dec,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
MRclass = "42A10 (41A10)",
MRnumber = "85a:42002",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See corrigendum \cite{}.",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "07952",
jrldate = "Dec. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Johnson:1983:MGC,
author = "Gary M. Johnson",
title = "Multiple-grid convergence acceleration of viscous and
inviscid flow computations",
journal = j-APPL-MATH-COMP,
volume = "13",
number = "3--4",
pages = "375--398",
month = nov,
year = "1983",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
MRclass = "76-08",
MRnumber = "84m:76010",
bibdate = "Thu Feb 27 09:47:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Kershaw:1983:SEW,
author = "D. Kershaw",
title = "Some extensions of {W. Gautschi}'s inequalities for
the gamma function",
journal = j-MATH-COMPUT,
volume = "41",
number = "164",
pages = "607--611",
month = oct,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A15 (26D20 65D20)",
MRnumber = "84m:33003",
MRreviewer = "P. Anandani",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Lehnhoff:1983:NPT,
author = "H.-G Lehnhoff",
title = "A new proof of {Teljakowskii}'s theorem",
journal = j-J-APPROX-THEORY,
volume = "38",
number = "2",
pages = "177--181",
month = jun,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "07897",
jrldate = "June 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Lehnhoff:1983:SPF,
author = "H.-G Lehnhoff",
title = "A simple proof of a {A.F. Timan}'s theorem",
journal = j-J-APPROX-THEORY,
volume = "38",
number = "2",
pages = "172--176",
month = jun,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory",
guideno = "07896",
jrldate = "June 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Little:1983:CCS,
author = "F. Little",
editor = "Robert E. Barnhill and Wolfgang Boehm",
booktitle = "Surfaces in computer aided geometric design:
proceedings of a conference held at Mathematisches
Forschungsinstitut Oberwolfach, F.R.G., April 25--30,
1982, organized by Wolfgang Boehm and Josef Hoschek",
title = "Convex combination surfaces",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "99--109",
year = "1983",
ISBN = "0-444-86550-0",
ISBN-13 = "978-0-444-86550-2",
LCCN = "T385 .S827 1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bookpages = "xvi + 215",
catcode = "G.1.1; G.1.1; G.1.2",
CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas;
G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Interpolation formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, Interpolation,
Smoothing; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory",
guideno = "13093",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@TechReport{Lutskii:1983:VFT,
author = "G. M. Lutski{\u{\i}} and O. I. Penchev",
title = "{\cyr Vychislenie {\`e}lementarnykh
funktsi{\u{\i}}metodom tsifra za tsifro{\u{\i}}v
izbytochnykh sistemakh schisleniya}. ({Russian})
[Calculation of elementary functions by the
digit-by-digit method in redundant number systems]",
type = "Preprint",
number = "83-22",
institution = "Akad. Nauk Ukrain. SSR, Inst. Kibernet.",
address = "Kiev, USSR",
pages = "30",
year = "1983",
MRclass = "65D20",
MRnumber = "719 021",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Mason:1983:CBF,
author = "Janet P. Mason",
title = "Cylindrical {Bessel} functions for a large range of
complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "30",
number = "1",
pages = "1--11",
month = jul # "\slash " # aug,
year = "1983",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(83)90116-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:05 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583901169",
abstract = "The evaluation of Bessel functions of the first and
second kinds, covering a wide range of complex
arguments and integer orders, is required in the
determination of the intensity of acoustic reflection
from absorbing bodies. Numerical problems associated
with the calculations are discussed and various means
by which these problems have been overcome are
explained. The numerical methods used in calculating
the Bessel functions of the first, second and third
kinds are given, as well as sample results and
numerical checks in the form of computer plots and
printouts.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@TechReport{McCurdy:1983:ACD,
author = "A. McCurdy and K. C. Ng and Beresford N. Parlett",
title = "Accurate computation of divided differences of the
exponential function",
type = "Report",
number = "PAM-160",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1983",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Meister:1983:MYF,
author = "B. Meister",
title = "On {Murphy}'s yield formula",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "545--548",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "B.7.1; G.1.2",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Input/Output
circuits; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Input/Output circuits; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "theory; design; reliability",
guideno = "06316",
jrldate = "Nov. 1983",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Mlodzki:1983:PPC,
author = "J. Mlodzki and J. Kuszkowski and M. Suffczynski",
title = "A {Pascal} program for calculating the reduced
{Coulomb} {Green}'s functions and their partial waves",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "4",
pages = "341--350",
month = jun,
year = "1983",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Feb 24 18:49:59 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900139",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
}
@Article{Moler:1983:RSR,
author = "Cleve B. Moler and Donald Morrison",
title = "Replacing Square Roots by {Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "577--581",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Dubrulle:1983:CNM} and generalization
\cite{Jamieson:1989:RCI}.",
URL = "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
abstract = "An algorithm is presented for computing a 'Pythagorean
sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
a and b without computing their squares or taking a
square root. No destructive floating point overflows or
underflows are possible. The algorithm can be extended
to compute the Euclidean norm of a vector. The
resulting subroutine is short, portable, robust, and
accurate, but not as efficient as some other
possibilities. The algorithm is particularly attractive
for computers where space and reliability are more
important than speed",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
corpsource = "Dept. of Computer Sci., Univ. of New Mexico,
Albuquerque, NM, USA",
keywords = "algorithms; digital arithmetic; Euclidean norm;
floating-point arithmetic; iterative methods;
performance; Pythagorean sums; subroutine; vector",
review = "ACM CR 8406-0463",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials \\ F.2.2 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Monk:1983:SFE,
author = "P. B. Monk",
title = "Some finite element methods for the approximation of
the biharmonic equation",
type = "{Ph.D} Thesis",
school = "Rutgers University, The State University of New
Jersey",
address = "New Brunswick, NJ, USA",
pages = "242",
year = "1983",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.8; G.1.2",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Finite
element methods; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Finite element methods;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "design; algorithms; experimentation",
guideno = "15929",
source = "UMI order no. DA8308441",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Nave:1983:ITF,
author = "Rafi Nave",
key = "Nav83",
title = "Implementation of Transcendental Functions on a
Numerics Processor",
journal = j-MICROPROC-MICROPROG,
volume = "11",
pages = "221--225",
year = "1983",
CODEN = "MMICDT",
ISSN = "0165-6074",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Prosser:1983:NCS,
author = "C. J. Prosser",
title = "A note on computing the square root of an integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compj.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
keywords = "binary; computer; fixed-point number; integer;
interactive methods; iterative methods; PASCAL; Pascal
implementation; square root; subroutines; successive
subtraction",
treatment = "P Practical",
}
@Article{Sidi:1983:ZSP,
author = "Avram Sidi and Doron S. Lubinsky",
title = "On the zeros of some polynomials that arise in
numerical quadrature and convergence acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "2",
pages = "400--405",
month = apr,
year = "1983",
CODEN = "SJNAAM",
DOI = "http://dx.doi.org/10.1137/0720028",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65H05 (65D30)",
MRnumber = "694528 (84f:65046)",
MRreviewer = "J. G. Herriot",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
keywords = "convergence acceleration",
}
@Article{Talman:1983:LSC,
author = "James D. Talman",
title = "{LSFBTR}: a subroutine for calculating spherical
{Bessel} transforms",
journal = j-COMP-PHYS-COMM,
volume = "30",
number = "1",
pages = "93--99",
month = jul # "\slash " # aug,
year = "1983",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:05 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583901261",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Temme:1983:NCC,
author = "N. M. Temme",
title = "The numerical computation of the confluent
hypergeometric function ${U}(a,\,b,\,z)$",
journal = j-NUM-MATH,
volume = "41",
number = "1",
pages = "63--82",
month = apr,
year = "1983",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20 (33A30 65D15)",
MRnumber = "84g:65030",
MRreviewer = "H. E. Fettis",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "Math. Centrum, Amsterdam, Netherlands",
keywords = "ALGOL 60 procedures; asymptotic expansions; confluent
hypergeometric function; function computation; function
evaluation; Miller algorithm; subroutines",
treatment = "P Practical; T Theoretical or Mathematical",
}
@TechReport{Temme:1983:TTR,
author = "N. M. Temme",
title = "Traces to {Tricomi} in recent work on special
functions and asymptotics of integrals",
type = "Report",
number = "TW 239/83",
institution = "Stichting mathematisch Centrum",
address = "Amsterdam, The Netherlands",
pages = "15",
year = "1983",
LCCN = "A1 M462 TW239/83",
bibdate = "Sat Oct 30 18:29:48 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Volz:1983:CAA,
author = "H. V{\"o}lz",
title = "{{CORDIC} und {\"a}hnliche Algorithmen der elementaren
Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
\toenglish {CORDIC and Similar Algorithms for
Elementary Functions with Particular Aptitude for
Microcomputers} \endtoenglish",
journal = j-NACH-ELEK,
volume = "33",
number = "12",
pages = "506--510",
month = "????",
year = "1983",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Xu:1983:HPG,
author = "Xian Yu Xu and Jia Kai Li and Gui Jing Xiong and Guo
Liang Xu and Chun Qing Lu",
title = "High-precision generation of elementary functions.
({Chinese})",
journal = "Appl. Math. Math. Comput.",
volume = "6",
pages = "24--32",
year = "1983",
MRclass = "65D20",
MRnumber = "86e:65031",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ardill:1984:ABF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Accurate {Bessel} functions {$J_n(z)$}, {$Y_n(z)$},
{$H_n^{(1)}(z)$} and {$H_n^{(2)}(z)$} of integer order
and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-559--C-559",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82734-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827344",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Ardill:1984:BFC,
author = "W. B. Ardill and K. J. M. Moriarty",
title = "The {Bessel} functions {$J_0$} and {$J_1$} of complex
argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
pages = "C-409--C-409",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82619-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ardill:1984:SBF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Spherical {Bessel} functions $j_n$ and $y_n$ of
integer order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
pages = "C-466--C-466",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82666-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "No code shown, but uses formulas from
\cite{Abramowitz:1964:HMF} for evaluations. Function
name is {\tt sphbes}.",
}
@Article{Bardin:1984:CFE,
author = "C. Bardin and Y. Dandeu and L. Gauthier and J.
Guillermin and T. Lena and J. -M. Pernet and H. H.
Wolter and T. Tamura",
title = "{Coulomb} functions in entire $(\eta, \pi)$-plane",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-125--C-126",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:06 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584823826",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Barnett:1984:CCB,
author = "A. R. Barnett",
title = "{Coulfg}: {Coulomb} and {Bessel} functions and their
derivatives, for real arguments, by {Steed}'s method",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-812--C-813",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82930-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829306",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Barnett:1984:CWF,
author = "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
B. Goldfarb",
title = "{Coulomb} wave functions for all real $\eta$ and
$\rho$",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-285",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:15 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584825151",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Barnett:1984:KCF,
author = "A. R. Barnett",
title = "{Klein}: {Coulomb} functions for real $\lambda$ and
positive energy to high accuracy",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-753",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828842",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Barnett:1984:RMR,
author = "A. R. Barnett",
title = "{RCWFF} --- a modification of the real {Coulomb}
wavefunction program {RCWFN}",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-370",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:24 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584825850",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Bell:1984:CFN,
author = "K. L. Bell and N. S. Scott",
title = "{Coulomb} functions (negative energies)",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-648",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828088",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@InCollection{Berges:1984:AFE,
author = "J. C. Berges",
booktitle = "Space mathematics",
title = "Arithm{\'e}tique et fonctions {\'e}l{\'e}mentaires sur
mini-micro calculateurs. ({French}) [Arithmetic and
elementary functions on mini-micro computers]",
publisher = "C{\'e}padu{\`e}s",
address = "Toulouse, France",
pages = "193--229",
year = "1984",
MRclass = "65-01 (65-04)",
MRnumber = "849 200",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Berndt:1984:APA,
author = "Bruce C. Berndt and Larry A. Goldberg",
title = "Analytic properties of arithmetic sums arising in the
theory of the classical theta functions",
journal = j-SIAM-J-MATH-ANA,
volume = "15",
number = "1",
pages = "143--150",
month = jan,
year = "1984",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "11A15 (11A25 11F27)",
MRnumber = "85d:11008",
MRreviewer = "T. M. Apostol",
bibdate = "Sun Nov 28 19:23:19 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/15/1;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Black:1984:NIS,
author = "Cheryl M. Black and Robert P. Burton and Thomas H.
Miller",
title = "The Need for an Industry Standard of Accuracy for
Elementary-Function Programs",
journal = j-TOMS,
volume = "10",
number = "4",
pages = "361--366",
month = dec,
year = "1984",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20",
MRnumber = "792 000",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1.2; G.4",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, MATHEMATICAL
SOFTWARE, Efficiency",
genterm = "theory; algorithms; reliability; standardization",
guideno = "02897",
jrldate = "Dec. 1984",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE",
}
@Article{Borwein:1984:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic-Geometric Mean and Fast Computation of
Elementary Functions",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
MRclass = "65D20 (26A09)",
MRnumber = "86d:65029",
MRreviewer = "S. Conde",
bibdate = "Mon Jan 20 10:31:25 MST 1997",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We produce a self contained account of the
relationship between the Gaussian arithmetic-geometric
mean iteration and the fast computation of elementary
functions. A particularly pleasant algorithm for pi is
one of the by-products.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
classification = "723; 921",
journalabr = "SIAM Rev",
keywords = "arithmetic-geometric mean; calculation of pi;
computational methods; elliptic functions; Iterative
Methods; mathematical techniques; numerical
mathematics",
}
@Article{Campbell:1984:BFRa,
author = "J. B. Campbell",
title = "{Bessel} Functions {$J_\nu(x)$} of real order and real
argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-583--C-583",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82756-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827563",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Campbell:1984:BFZ,
author = "J. B. Campbell",
title = "{Bessel} functions ${I_\nu(z)$} and {$K_\nu(z)$} of
real order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-747--C-748",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828805",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Coleman:1984:FSB,
author = "J. P. Coleman",
title = "A {Fortran} subroutine for the {Bessel} function
{$J_n(x)$} of order $0$ to $10$",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-654--C-654",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82814-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fortran2.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828143",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
remark = "No code shown, but sums two separate Chebyshev series,
one for $x$ in $[0,8]$, and a second for $x$ in
$(8,\infty)$. Function name is {\tt realjn}.",
}
@Article{Delic:1984:CSS,
author = "G. Delic",
title = "{Chebyshev} sries for the spherical {Bessel} function
$l(r)$",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-577--C-577",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(84)82751-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827514",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Dhanoa:1984:BPE,
author = "M. S. Dhanoa and J. France",
title = "A {BASIC} program for the evaluation of the gamma
functions",
journal = j-J-APPL-STAT,
volume = "11",
number = "2",
pages = "225--228",
year = "1984",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/02664768400000021",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:15:50 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
onlinedate = "24 May 2006",
}
@Article{Dutka:1984:EHH,
author = "Jacques Dutka",
title = "The early history of the hypergeometric function",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "31",
number = "1",
pages = "15--34",
month = mar,
year = "1984",
CODEN = "AHESAN",
DOI = "http://dx.doi.org/10.1007/BF00330241",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
MRclass = "01A50 (33-03)",
MRnumber = "769538 (86d:01010)",
MRreviewer = "Willard Parker",
bibdate = "Fri Feb 4 21:50:21 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=31&issue=1;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=31&issue=1&spage=15",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
MRtitle = "The early history of the hypergeometric function",
}
@Article{Fransen:1984:CMM,
author = "Arne Frans{\'e}n and Staffan Wrigge",
title = "Calculation of the moments and the moment generating
function for the reciprocal gamma distribution",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "601--616",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (60E10 62E15 65U05)",
MRnumber = "86f:65042a",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C1210B (Reliability theory); C4130 (Interpolation and
function approximation)",
corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden",
keywords = "kurtosis; moment generating function; moments;
polynomials; reciprocal gamma distribution; reliability
theory; skewness; variance",
treatment = "T Theoretical or Mathematical",
}
@Article{Glaeske:1984:LTS,
author = "H.-J. Glaeske and O. I. Mari{\v{c}}ev",
title = "The {Laguerre} transform of some elementary
functions",
journal = j-Z-ANAL-ANWEND,
volume = "3",
number = "3",
pages = "237--244",
year = "1984",
ISSN = "0232-2064",
MRclass = "44A15 (34A10)",
MRnumber = "86a:44005",
MRreviewer = "Ram Kishore Saxena",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Grodd:1984:REN,
author = "Laurence W. Grodd and Charles M. Patton",
title = "{ROM} extends numerical function set of handheld
computer",
journal = j-HEWLETT-PACKARD-J,
volume = "35",
number = "7",
pages = "25--36",
month = jul,
year = "1984",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1984-07.pdf",
abstract = "The plug-in math PAC for HP's new HP-71B Handheld
Computer further extends the HP-71B's comprehensive
standard numerical function set to provide a
mathematical tool of unprecedented capability and power
in a personal machine. Full use of complex variables,
integration, matrix algebra, and polynomial root
finding are some of the capabilities provided by this
plug-in module.",
acknowledgement = ack-nhfb,
affiliation = "Hewlett--Packard Co, Corvallis, OR, USA",
affiliationaddress = "Hewlett--Packard Co, Corvallis, OR, USA",
classcodes = "C7310 (Mathematics computing)",
classification = "723",
journalabr = "Hewlett Packard J",
keywords = "complex; complex variables; computers, miniature; data
storage, digital --- Fixed; data type; extended I/O
functions; fast Fourier transform; handheld computer;
HP-71B hand-held computer; matrix operations; numerical
analysis; numerical function set; polynomial; read-only
storage; ROM; root finder",
remark = "The paper notes: ``Completely support provisions of
the proposed IEEE floating-point mathematics standard.
\ldots{} an HP-71B REAL variable --- a 12-digit
mantissa and a three-digit exponent in the range from
$-499$ to $499$. Each part of a COMPLEX SHORT variable
or array element has the same precision as an HP-71B
SHORT variable --- a five-digit mantissa and a
three-digit exponent in the range from $-499$ to $499$.
Of course, denormalized numbers, Inf (infinity), and
NaNs (not-a-numbers) are also permitted.''",
treatment = "P Practical; X Experimental",
}
@Article{Gustafson:1984:SCC,
author = "Sven-{\AA}ke Gustafson",
title = "On the stability of a class of convergence
acceleration methods for power series",
journal = j-BIT,
volume = "24",
number = "4",
pages = "510--519",
month = dec,
year = "1984",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01934909",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65B10",
MRnumber = "764823 (86c:65006)",
MRreviewer = "D. Levin",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=4&spage=510",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
keywords = "convergence acceleration",
}
@Article{Karp:1984:ELS,
author = "A. H. Karp",
title = "Exponential and Logarithm by Sequential Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "5",
pages = "462--464",
month = may,
year = "1984",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1984.1676464",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:52 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676464",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Kolbig:1984:PCL,
author = "K. S. K{\"o}lbig",
title = "Programs for computing the logarithm of the gamma
function, and the digamma function, for complex
argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-152",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:06 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584824042",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Laforgia:1984:FIG,
author = "Andrea Laforgia",
title = "Further Inequalities for the Gamma Function",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "597--600",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A15",
MRnumber = "85i:33001",
MRreviewer = "H. E. Fettis",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math., Univ. of Torino, Torino, Italy",
keywords = "gamma function; inequalities; polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{McCurley:1984:EE,
author = "Kevin S. McCurley",
title = "Explicit Estimates for $\theta (x; 3, l)$ and $\psi
(x; 3, l)$",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "287--296",
month = jan,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11N56",
MRnumber = "85g:11085",
MRreviewer = "G. J. Rieger",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Maths., Michigan State Univ., East Lansing,
MI, USA",
keywords = "arithmetic progressions; Chebyshev approximation;
Chebyshev functions; Dirichlet L-; explicit estimates;
functions; prime number; theorem; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Moon:1984:AFC,
author = "Wooil Moon",
title = "{Airy} function with complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-692",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828428",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Nesbet:1984:ARI,
author = "R. K. Nesbet",
title = "Algorithms for regular and irregular {Coulomb} and
{Bessel} functions",
journal = j-COMP-PHYS-COMM,
volume = "32",
number = "4",
pages = "341--347",
month = jul,
year = "1984",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(84)90051-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465584900511",
abstract = "Algorithms for computing Coulomb--Bessel functions are
considered, with emphasis on obtaining accurate values
when the argument $x$ is inside the classical turning
point $x\lambda$. Algorithms of Barnett et al. for the
generalized Coulomb functions and their derivatives are
discussed in the context of the phase integral
formalism. Modified or alternative algorithms are
considered that are designed to be valid for all values
of argument $x$ and index $\lambda$ for the functions
$F_\lambda(x)$, $G_\lambda(x)$. An algorithm for
accelerating convergence of a power series by
conversion to a continued fraction is presented, and is
applied to the evaluation of spherical Bessel
functions. An explicit formula for the integrand of the
phase integral is presented for spherical Bessel
functions. The methods considered need to be augmented
by an efficient algorithm for computing the logarithmic
derivative of $G_0 + iF_0$ for Coulomb functions when
$x$ is smaller than the charge parameter $\eta$.",
acknowledgement = ack-nhfb,
}
@Article{Newman:1984:ABS,
author = "J. N. Newman",
title = "Approximations for the {Bessel} and {Struve}
functions",
journal = j-MATH-COMPUT,
volume = "43",
number = "168",
pages = "551--556",
month = oct,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33A40)",
MRnumber = "86c:65021",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C1120 (Mathematical analysis); C4130 (Interpolation and
function approximation)",
corpsource = "Dept. of Ocean Eng., MIT, Cambridge, MA, USA",
keywords = "accuracy; Bessel functions; function approximation;
functions; IBM PC computer; minimax; polynomial
approximations; polynomials; rational-fraction
approximations; single-precision computations; Struve",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Ng:1984:DAA,
author = "K. C. Ng",
title = "Contributions to the computation of the matrix
exponential",
type = "Report",
number = "PAM-212",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = feb,
year = "1984",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Based on the author's Ph.D. thesis.",
acknowledgement = ack-nhfb,
keywords = "$\exp(Bt)$",
}
@Article{Nishimoto:1984:TFD,
author = "Katsuyuki Nishimoto",
title = "Tables of fractional differintegrations of elementary
functions",
journal = "J. College Engrg. Nihon Univ. Ser. B",
volume = "25",
pages = "41--46",
year = "1984",
ISSN = "0285-6182",
MRclass = "30E20 (26A33)",
MRnumber = "85f:30065",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Noble:1984:CPE,
author = "C. J. Noble and I. J. Thompson",
title = "{COULN}, a program for evaluating negative energy
{Coulomb} functions",
journal = j-COMP-PHYS-COMM,
volume = "33",
number = "4",
pages = "413--419",
month = oct,
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Feb 24 13:39:14 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465584901462",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Piessens:1984:ACB,
author = "R. Piessens",
title = "Automatic computation of {Bessel} function integrals",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-791",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S001046558482915X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Piessens:1984:CSA,
author = "R. Piessens",
title = "{Chebyshev} series approximations for the zeros of the
{Bessel} functions",
journal = j-J-COMPUT-PHYS,
volume = "53",
number = "1",
pages = "188--192",
month = jan,
year = "1984",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(84)90060-3",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:18 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999184900603",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Piessens:1984:SEF,
author = "R. Piessens",
title = "A Series Expansion for the First Positive Zero of the
{Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "195--197",
month = jan,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40 (65D20)",
MRnumber = "84m:33014",
MRreviewer = "M. E. Muldoon",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
annote = "Gives explicit series for first positive zero for 4
terms, using REDUCE.",
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Leuven, Heverlee,
Belgium",
keywords = "Bessel functions; poles and zeros; positive zero;
Reduce; series (mathematics); series expansion",
treatment = "T Theoretical or Mathematical",
}
@Article{Schmidt:1984:TAI,
author = "J. W. Schmidt",
title = "Two-Sided Approximations of Inverses, Square Roots and
{Cholesky} Factors",
journal = "Comput. Math., Banach Center Publ.",
volume = "13",
pages = "483--497",
year = "1984",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr,
}
@Article{Seaton:1984:CFA,
author = "M. J. Seaton",
title = "{Coulomb} functions analytic in the energy",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-771",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828994",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Takemasa:1984:CFC,
author = "T. Takemasa and T. Tamura and H. H. Wolter",
title = "{Coulomb} functions with complex angular momenta",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-562",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S001046558482737X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Talman:1984:LSC,
author = "James D. Talman",
title = "{LSFBTR}: a subroutine for calculating spherical
{Bessel} transforms",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-903",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584830027",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Tamura:1984:CFC,
author = "Taro Tamura and Frank Rybicki",
title = "{Coulomb} functions for complex energies",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-5",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:55:58 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584822766",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Trojan:1984:LBF,
author = "George M. Trojan",
title = "Lower Bounds and Fast Algorithms for Sequence
Acceleration",
journal = j-J-ACM,
volume = "31",
number = "2",
pages = "329--335",
month = apr,
year = "1984",
CODEN = "JACOAH",
ISSN = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Tight upper and lower bounds are obtained for sequence
accelerating. The lower bounds follow from a powerful
asymptotic adversary principle. Algorithms are
presented and shown to be almost optimal.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Western Ontario, Dep of Physics, London,
Ont, Can",
classification = "723",
journalabr = "J Assoc Comput Mach",
keywords = "Algorithms; computer programming; convergence
acceleration; lower bounds; sequence acceleration;
upper bounds",
}
@Book{vanderLaan:1984:CSF,
author = "C. G. van der Laan and N. M. Temme",
title = "Calculation of special functions: the gamma function,
the exponential integrals and error-like functions",
volume = "10",
publisher = "Centre for Mathematics and Computer Science,",
address = "Amsterdam, The Netherlands",
pages = "iv + 231",
year = "1984",
ISBN = "90-6196-277-3",
ISBN-13 = "978-90-6196-277-9",
LCCN = "QA1 M4591 no. 10",
bibdate = "Sat Oct 30 18:43:03 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "CWI tract / Centrum voor Wiskunde en Informatica",
acknowledgement = ack-nhfb,
}
@Article{vonGudenberg:1984:BMG,
author = "J. Wolff {von Gudenberg}",
title = "{Berechnung maximal genauer Standardfunktionen mit
einfacher Mantissenl{\"a}nge} \toenglish {Computation
of Maximally Accurate Elementary Functions Using Simple
Mantissa Length} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "26",
number = "5",
pages = "230--238",
month = oct,
year = "1984",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sun Oct 25 10:29:27 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Walmsley:1984:EEM,
author = "John L. Walmsley",
title = "On the efficient evaluation of modified {Bessel}
functions of zeroth and first orders for arguments of
the form $x \exp(i \pi / 4)$",
journal = j-J-COMPUT-PHYS,
volume = "56",
number = "2",
pages = "349--355",
month = nov,
year = "1984",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(84)90100-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:21 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999184901001",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Book{Wawrzynczyk:1984:GRS,
author = "Antoni Wawrzy{\'n}czyk and Aleksander Strasburger",
title = "Group representations and special functions",
volume = "8",
publisher = "D. Reidel",
address = "Dordrecht, The Netherlands",
pages = "xvi + 688",
year = "1984",
ISBN = "90-277-1269-7",
ISBN-13 = "978-90-277-1269-1",
LCCN = "QA171 .W3513 1984; QA1 M4281 v. 8",
bibdate = "Sat Oct 30 18:29:38 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematics and its applications. East European
series",
acknowledgement = ack-nhfb,
remark = "Translation of Polish title Wsp\'o\pm{}czesna teoria
funkcji specjalnych.",
subject = "Representations of groups; Functions, Special",
}
@Article{Wrigge:1984:NMG,
author = "Staffan Wrigge",
title = "A note on the moment generating function for the
reciprocal gamma distribution",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "617--621",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (60E10 62E15 65U05)",
MRnumber = "86f:65042b",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden",
keywords = "Euler--Maclaurin expansion; moment generating
function; polynomials; reciprocal gamma distribution",
treatment = "T Theoretical or Mathematical",
}
@Article{Akrivis:1985:ENC,
author = "G. Akrivis",
title = "The error norm of certain {Gaussian} quadrature
formulae",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "513--519",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D32",
MRnumber = "87a:65051",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Math. Inst., Munchen Univ., West Germany",
keywords = "error analysis; error functional; error norm; function
approximation; Gaussian quadrature formulae;
integration; weight functions; wide class",
treatment = "T Theoretical or Mathematical",
}
@Article{Bank:1985:SEM,
author = "Randolph E. Bank and Craig C. Douglas",
title = "Sharp estimates for multigrid rates of convergence
with general smoothing and acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "22",
number = "4",
pages = "617--633",
month = aug,
year = "1985",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
MRclass = "65F10 (65N20)",
MRnumber = "86j:65037",
MRreviewer = "L. W. Ehrlich",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Bannur:1985:VIS,
author = "J. Bannur and A. Varma",
title = "The {VLSI} Implementation of a Square Root Algorithm",
crossref = "Hwang:1985:PSC",
pages = "159--165",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
abstract = "VLSI implementation of a square root algorithm is
studied. Two possible implementations of the basic
nonrestoring algorithm are presented --- the second is
more area-efficient and modular than the first. The
implementations are simple and easy to control, but, at
the same time, are more area-time efficient than many
existing designs. A hardware algorithm suited to
microprogram implementation is also given. Extension of
the algorithms to achieve $1/2$-bit precision is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Borodin:1985:DND,
author = "Allan Borodin and Ronald Fagin and John E. Hopcroft
and Martin Tompa",
title = "Decreasing the Nesting Depth of Expressions Involving
Square Roots",
journal = j-J-SYMBOLIC-COMP,
volume = "1",
number = "2",
pages = "169--188",
month = jun,
year = "1985",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
MRclass = "68Q40 (12F05)",
MRnumber = "87a:68087",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Simplification",
}
@Article{Brezinski:1985:CAM,
author = "Claude Brezinski",
title = "Convergence acceleration methods: the past decade",
journal = j-J-COMP-APPL-MATH,
volume = "12--13",
number = "??",
pages = "19--36",
month = may,
year = "1985",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0377-0427(85)90005-6",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65Bxx (65J05)",
MRnumber = "793942 (86f:65019)",
bibdate = "Thu Dec 01 10:11:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
keywords = "convergence acceleration",
remark = "Proceedings of the international conference on
computational and applied mathematics (Leuven, 1984).",
}
@Article{Carlson:1985:AEF,
author = "B. C. Carlson and John L. Gustafson",
title = "Asymptotic expansion of the first elliptic integral",
journal = j-SIAM-J-MATH-ANA,
volume = "16",
number = "5",
pages = "1072--1092",
month = sep,
year = "1985",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A25 (41A60)",
MRnumber = "87d:33002",
MRreviewer = "Kusum Soni",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Cathey:1985:ISR,
author = "James Cathey",
title = "68000 Integer square root routine in {16BST}",
journal = j-DDJ,
volume = "10",
number = "5",
pages = "118--??",
month = may,
year = "1985",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Conover:1985:AHS,
author = "B. Conover and D. L. Gustafson",
title = "An Algorithm for High Speed Square Roots",
crossref = "IEEE:1985:ERC",
pages = "19--21",
year = "1985",
bibdate = "Fri Jun 11 18:04:41 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Frenzen:1985:NAE,
author = "C. L. Frenzen and R. Wong",
title = "A note on asymptotic evaluation of some {Hankel}
transforms",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "537--548",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "41A60 (44A15 65R10)",
MRnumber = "87c:41024",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0230 (Integral transforms); B0290Z (Other numerical
methods)C1130 (Integral transforms); C4190 (Other
numerical methods)",
corpsource = "Dept. of Math., British Columbia Univ., Vancouver, BC,
Canada",
keywords = "asymptotic expansion; Bessel function; Bessel
functions; growth condition; Hankel transforms;
meromorphic function; transforms",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gal:1985:CEF,
author = "Shmuel Gal",
title = "Computing Elementary Functions: {A} New Approach for
Achieving High Accuracy and Good Performance",
crossref = "Miranker:1985:ASC",
pages = "1--16",
year = "1985",
bibdate = "Sat Nov 09 07:42:53 2002",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Gustafson:1985:SCA,
author = "Sven-{\AA}ke Gustafson",
title = "Stable convergence acceleration using {Laplace}
transforms",
journal = j-NUM-MATH,
volume = "47",
number = "3",
pages = "387--394",
month = nov,
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
MRclass = "65B10 (65D30)",
MRnumber = "86m:65009",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Dept. of Numerical Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
keywords = "convergence acceleration; Laplace transforms; power
series; quadrature schemes; series (mathematics);
stable convergence acceleration",
treatment = "T Theoretical or Mathematical",
}
@Article{Hill:1985:RCS,
author = "I. D. Hill and M. C. Pike",
title = "Remark on ``{Algorithm 299: Chi-Squared Integral}''",
journal = j-TOMS,
volume = "11",
number = "2",
pages = "185--185",
month = jun,
year = "1985",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Feb 06 05:28:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
}
@Article{Hull:1985:PRV,
author = "T. E. Hull and A. Abrham",
title = "Properly Rounded Variable Precision Square Root",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "229--237",
month = sep,
year = "1985",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D15 (65G05)",
MRnumber = "87a:65041",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/;
http://www.acm.org/pubs/toc/Abstracts/toms/214413.html",
abstract = "The square root function presented here returns a
properly rounded approximation to the square root of
its argument, or it raises an error condition if the
argument is negative. {\em Properly rounded} means
rounded to the nearest, or to nearest even in case of a
tie. It is {\em variable precision} in that it is
designed to return a $p$-digit approximation to a
$p$-digit argument, for any $p$ \$>\$ 0. (Precision $p$
means $p$ decimal digits.) The program and the analysis
are valid for all $p$ \$>\$ 0, but current
implementations place some restrictions on $p$.",
acknowledgement = ack-nhfb,
catcode = "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
CRclass = "G.4 Algorithm analysis; G.4 Verification; G.1.0
General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.4 Certification and testing; G.1.0 General; G.1.0
Error analysis",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis; Mathematics of Computing,
MATHEMATICAL SOFTWARE, Verification; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Error
analysis",
genterm = "algorithms; verification",
guideno = "02789",
jrldate = "Sept. 1985",
keywords = "algorithms; verification",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@Article{Humblet:1985:BFE,
author = "J. Humblet",
title = "{Bessel} function expansions of {Coulomb} wave
functions",
journal = j-J-MATH-PHYS,
volume = "26",
number = "4",
pages = "656--659",
month = apr,
year = "1985",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.526602",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C05 (33A40 81G45)",
MRnumber = "87c:81034",
bibdate = "Mon Oct 31 11:57:19 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p656_s1",
acknowledgement = ack-nhfb,
pagecount = "4",
}
@Article{Kravchuk:1985:ACE,
author = "V. R. Kravchuk",
title = "Approximation of certain elementary functions by
rational functions of order $(n,2)$. ({Russian})",
journal = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
volume = "18",
pages = "7--40",
year = "1985",
MRclass = "41A25 (41A10)",
MRnumber = "87b:41017",
MRreviewer = "R. Smarzewski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kravchuk:1985:EAE,
author = "V. R. Kravchuk",
title = "Effective approximation of elementary functions by
rational polynomials of order $(n,1)$. ({Russian})",
journal = "Ukrain. Mat. Zh.",
volume = "37",
number = "2",
pages = "175--180, 270",
year = "1985",
MRclass = "41A20 (41A25)",
MRnumber = "86h:41013",
MRreviewer = "Miguel A. Jim{\'e}nez Pozo",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lazard:1985:PFD,
author = "Daniel Lazard",
title = "Primitives des fonctions {\'e}l{\'e}mentaires
(d'apr{\`e}s {Risch} et {Davenport}). ({French})
[Primitives of elementary functions (following {Risch}
and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No.
121-122}",
journal = "Ast{\'e}risque",
volume = "121--122",
pages = "295--308",
year = "1985",
MRclass = "12H05 (12-04)",
MRnumber = "86k:12010",
MRreviewer = "J. H. Davenport",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lewanowicz:1985:RRH,
author = "Stanis{\l}aw Lewanowicz",
title = "Recurrence relations for hypergeometric functions of
unit argument",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "521--535",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65Q05)",
MRnumber = "86m:33004",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
keywords = "(mathematics); convergence of numerical methods;
hypergeometric function; numerical analysis; recurrence
relation; series; unit argument",
treatment = "T Theoretical or Mathematical",
}
@Article{Lo:1985:GPB,
author = "Hao-Yung Lo and Y. Aoki",
title = "Generation of a Precise Binary Logarithm with
Difference Grouping Programmable Logic Array",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "681--691",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1985.1676614",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676614",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Majerski:1985:SRA,
author = "S. Majerski",
title = "Square-Rooting Algorithms for High-Speed Digital
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "724--733",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1985.1676618",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Martin:1985:FAB,
author = "Pablo Mart{\'\i}n and Antonio L. Guerrero",
title = "Fractional approximations to the {Bessel} function
{$J_0(x)$}",
journal = j-J-MATH-PHYS,
volume = "26",
number = "4",
pages = "705--707",
month = apr,
year = "1985",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.526610",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A21 (33A40)",
MRnumber = "86g:41031",
MRreviewer = "Hans-J{\"u}rgen Albrand",
bibdate = "Mon Oct 31 11:57:19 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p705_s1",
acknowledgement = ack-nhfb,
pagecount = "3",
}
@Article{Milgram:1985:GIE,
author = "M. S. Milgram",
title = "The Generalized Integro-Exponential Function",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "443--458",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A70 (65D15)",
MRnumber = "86c:33024",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation)",
corpsource = "AECL, Chalk River, Ont., Canada",
keywords = "exponential function; exponential integral;
first-order functions; function; function
approximation; function evaluation; generalized
integro-; incomplete gamma; minimax; rational minimax
approximations; techniques",
treatment = "T Theoretical or Mathematical",
}
@Article{Muller:1985:DBC,
author = "Jean-Michel Muller",
title = "Discrete basis and computation of elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "857--862",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1985.1676643",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D20 (65V05)",
MRnumber = "87e:65016",
MRreviewer = "D. Zwick",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
abstract = "We give necessary and sufficient conditions in order
that the infinite product or sum of the terms of a
positive decreasing sequence generates the reals in a
given interval.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@InCollection{Muller:1985:RNR,
author = "Jean-Michel Muller",
booktitle = "Seminar on number theory, 1984--1985 (Talence,
1984/1985),",
title = "Repr{\'e}sentation des nombres r{\'e}els et calcul des
fonctions {\'e}l{\'e}mentaires. ({French})
[Representation of real numbers and calculation of
elementary functions]",
volume = "12",
publisher = "Univ. Bordeaux {I}",
address = "Talence, France",
pages = "22",
year = "1985",
MRclass = "26-04 (11B13 11B34 26A09)",
MRnumber = "87k:26001",
MRreviewer = "S. L. Segal",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "From the MRreview: ``About one third of the paper is
devoted to algorithms for calculating quantities like
square root, exponential, logarithm, or trigonometric
funtions, using discrete bases. Indeed, the major
motivation for the present paper is obtaining simple
algorithms which can easily be realized by
hardware.''",
}
@TechReport{Parlett:1985:DAA,
author = "Beresford N. Parlett and K. C. Ng",
title = "Development of an accurate algorithm for
{$\exp(Bt)$}",
type = "Technical Report",
number = "PAM-294",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = aug,
year = "1985",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Peralta:1985:TRN,
author = "Rene Caupolican Peralta",
title = "Three results in number theory and cryptography: {A}
new algorithm to compute square roots modulo a prime
number; On the bit complexity of the discrete
logarithm; {A} framework for the study of
cryptoprotocols",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "52",
month = dec,
year = "1985",
LCCN = "????",
bibdate = "Sat Oct 17 16:25:07 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cryptography.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations; dissertations, academic --- UCB ---
computer science --- 1981--1990; University of
California, Berkeley. computer science division --",
}
@Article{Pereira:1985:ECF,
author = "N. Costa Pereira",
title = "Estimates for the {Chebyshev} function $\psi(x)-\theta
(x)$",
journal = j-MATH-COMPUT,
volume = "44",
number = "169",
pages = "211--221",
month = jan,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11A25 (11N45 11Y35 33A70)",
MRnumber = "86k:11005",
bibdate = "Thu Jun 15 07:26:46 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See corrigendum \cite{Pereira:1987:CEC}.",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "Chebyshev approximation; Chebyshev function",
treatment = "T Theoretical or Mathematical",
}
@Article{Schoof:1985:ECF,
author = "Ren{\'e} Schoof",
title = "Elliptic Curves Over Finite Fields and the Computation
of Square Roots $\operatorname{mod} p$",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "483--494",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16 (11G20 14G15)",
MRnumber = "86e:11122",
MRreviewer = "Karl Rubin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0250 (Combinatorial mathematics); B0290D (Functional
analysis); C1160 (Combinatorial mathematics); C4120
(Functional analysis); C4240 (Programming and algorithm
theory)",
corpsource = "Amsterdam Univ., Netherlands",
keywords = "computational complexity; deterministic algorithm;
elliptic curve; F/sub q/-points; finite fields;
function evaluation; number theory; square roots mod p;
Weierstrass equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Spijker:1985:SRS,
author = "M. N. Spijker",
title = "Stepsize restrictions for stability of one-step
methods in the numerical solution of initial value
problems",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "377--392",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65L20 (65M10)",
MRnumber = "86j:65106",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); A0560
(Transport processes: theory); B0290F (Interpolation
and function approximation); B0290P (Differential
equations); C4130 (Interpolation and function
approximation); C4170 (Differential equations); C7320
(Physics and chemistry computing)",
corpsource = "Inst. of Appl. Math. and Comput. Sci., Leiden Univ.,
Netherlands",
keywords = "convection; convergence of numerical methods;
differential equations; diffusion;
diffusion-convection; error growth; initial value
problems; iterative methods; numerical solution;
partial; problem; stability of one-step methods;
stepsize restrictions",
treatment = "T Theoretical or Mathematical",
}
@Article{Sreedharan:1985:ASS,
author = "J. Sreedharan and A. Dhurkadas",
title = "8086 algorithm solves square roots",
journal = j-EDN,
volume = "30",
number = "7",
pages = "272",
month = apr,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "New Scalar and Vector Elementary Functions for the
{IBM System\slash 370}",
journal = j-IBM-JRD,
volume = "30",
number = "2",
pages = "126--144",
month = mar,
year = "1986",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "76W05",
MRnumber = "840 341",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See clarification \cite{Agarwal:1987:CNS}.",
abstract = "Algorithms have been developed to compute short-and
long-precision elementary functions: SIN, COS, TAN,
COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
ATAN2, and CABS, in scalar (28 functions) and vector
(22 functions) mode. They have been implemented as part
of the new VS FORTRAN library recently announced along
with the IBM 3090 Vector Facility. These algorithms are
essentially table-based algorithms. An important
feature of these algorithms is that they produce
bitwise-identical results on scalar and vector
System\slash 370 machines. Of these, for five functions
the computed value result is always the correctly
rounded value of the infinite-precision result. For the
rest of the functions, the value returned is one of the
two floating-point neighbors bordering the
infinite-precision result, which implies exact results
if they are machine-representable. For the five
correctly rounded elementary functions, scalar and
vector algorithms are designed independently to
optimize performance in each case.",
acknowledgement = ack-nhfb,
classification = "723",
journalabr = "IBM J Res Dev",
keywords = "algorithms; Algorithms; computer metatheory; computer
programming; computer programming languages ---
fortran; design; elementary functions; fortran library;
IBM System/370; infinite-precision result; measurement;
performance; table-based algorithms",
subject = "C.4 Computer Systems Organization, PERFORMANCE OF
SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms \\ F.3.3 Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Functional constructs \\ C.1.2
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Array and vector processors",
}
@Article{Amos:1986:APP,
author = "D. E. Amos",
title = "{Algorithm 644}: {A} Portable Package for {Bessel}
Functions of a Complex Argument and Nonnegative Order",
journal = j-TOMS,
volume = "12",
number = "3",
pages = "265--273",
month = sep,
year = "1986",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/7921.214331",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20",
MRnumber = "889 069",
bibdate = "Tue Mar 09 10:26:27 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also
\cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/",
abstract = "This algorithm is a package of subroutines for
Computing Bessel functions $H_{v}^{(1)}(z)$,
$H_{v}^{(2)}(z)$, $I_{v}(z)$, $J_{v}(z)$, $K_{v}(z)$,
$Y_{v}(z)$ and Airy functions $\mbox{Ai}(z)$,
$\mbox{Ai}'(z)$, $\mbox{Bi}(z)$, $\mbox{Bi}'(z)$ for
orders $v>=0$ and complex $z$ in $-\pi< \mbox{arg} z <=
\pi$. Eight callable subroutines and their
double-precision counterparts are provided. Exponential
scaling and sequence generation are auxiliary
options.",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.m}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Miscellaneous. {\bf G.m}: Mathematics of Computing,
MISCELLANEOUS.",
}
@Article{Andrews:1986:SCA,
author = "George E. Andrews and Ian P. Goulden and David M.
Jackson",
title = "{Shanks}' convergence acceleration transform,
{Pad{\'e}} approximants and partitions",
journal = j-J-COMB-THEORY-A,
volume = "43",
number = "1",
pages = "70--84",
year = "1986",
CODEN = "JCBTA7",
DOI = "http://dx.doi.org/10.1016/0097-3165(86)90024-5",
ISSN = "0097-3165",
ISSN-L = "0097-3165",
MRclass = "65B99 (11N99 11Y35)",
MRnumber = "859298 (88c:65005)",
MRreviewer = "Kenneth A. Jukes",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
keywords = "convergence acceleration",
}
@Article{Bustoz:1986:GFI,
author = "Joaquin Bustoz and Mourad E. H. Ismail",
title = "On Gamma Function Inequalities",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "659--667",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A15 (26D20)",
MRnumber = "87m:33002",
MRreviewer = "G. Gasper",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1130 (Integral transforms); C1140Z (Other and
miscellaneous)",
corpsource = "Dept. of Math., Arizona State Univ., Tempe, AZ, USA",
keywords = "gamma function inequalities; infinite divisibility;
Laplace; Laplace transforms; monotonic functions;
probability; probability distributions; quotients;
transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square Roots",
journal = j-DDJ,
volume = "11",
number = "3",
pages = "122--123, 106",
month = mar,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Dec 08 13:05:56 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cathey:1986:LEI,
author = "J. Cathey",
title = "Letter to the editor [Integer Square Root]",
journal = j-DDJ,
volume = "11",
number = "8",
pages = "14, 82--85",
month = aug,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 08 07:59:25 1994",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
and P. R. Turner",
title = "Generalized Exponential and Logarithmic Functions",
journal = j-COMP-MATH-APPL,
volume = "12",
number = "5--6",
pages = "1091--1101",
month = sep # "\slash " # dec,
year = "1986",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(86)90233-6",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "33A70 (39B10 65G05)",
MRnumber = "MR0871348 (88a:33027)",
bibdate = "Fri Jul 09 06:27:26 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalizations of the exponential and logarithmic
functions are defined and an investigation is made of
two possible versions of these functions. Some
applications are described, including computer
arithmetic, properties of very large and very small
numbers, and the determination of functional roots.",
acknowledgement = ack-nhfb,
}
@Article{Clenshaw:1986:UAR,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Unrestricted algorithms for reciprocals and square
roots",
journal = j-BIT,
volume = "26",
number = "4",
pages = "475--492",
month = dec,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01935054",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20",
MRnumber = "87k:65019",
MRreviewer = "Luciano Biasini",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
acknowledgement = ack-nhfb,
xxpages = "476--492??",
}
@Article{DiMarzio:1986:IPA,
author = "F. {Di Marzio}",
title = "An improved procedure for the accurate evaluation of
polygamma functions with integer and half-integer
argument",
journal = j-COMP-PHYS-COMM,
volume = "39",
number = "3",
pages = "343--345",
month = apr,
year = "1986",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:13 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465586900950",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Dutka:1986:SRT,
author = "Jacques Dutka",
title = "On square roots and their representations",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "36",
number = "1",
pages = "21--39",
month = mar,
year = "1986",
CODEN = "AHESAN",
DOI = "http://dx.doi.org/10.1007/BF00357439",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A05 (11-03 11A63)",
MRnumber = "863340 (87m:01003)",
MRreviewer = "Donald Cook",
bibdate = "Fri Feb 4 21:50:24 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
http://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
MRtitle = "On square roots and their representations",
}
@Article{Evans:1986:RIU,
author = "D. J. Evans and G. M. Megson",
title = "{Romberg} integration using systolic arrays",
journal = j-PARALLEL-COMPUTING,
volume = "3",
number = "4",
pages = "289--304",
month = oct,
year = "1986",
CODEN = "PACOEJ",
ISSN = "0167-8191",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "11019",
catcode = "G.1.1; G.1.2",
CRclass = "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Extrapolation; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory; design; algorithms",
guideno = "1986-10554",
journalabbrev = "Parallel Comput.",
jrldate = "Oct. 1986",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{FernandezVelicia:1986:HPA,
author = "F. J. {Fern{\'a}ndez Velicia}",
title = "High-precision analytic approximations for the
{Fermi--Dirac} functions by means of elementary
functions",
journal = "Phys. Rev. A (3)",
volume = "34",
number = "5",
pages = "4387--4395",
year = "1986",
CODEN = "PLRAAN",
ISSN = "1050-2947",
MRclass = "33A70 (82A05)",
MRnumber = "MR869021 (88b:33024)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review. A. Third Series",
}
@Article{Froman:1986:PIF,
author = "Per Olof Fr{\"o}man and Finn Karlsson and Staffan
Yngve",
title = "Phase-integral formulas for {Bessel} functions and
their relation to already existing asymptotic
formulas",
journal = j-J-MATH-PHYS,
volume = "27",
number = "11",
pages = "2738--2747",
month = nov,
year = "1986",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.527296",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A60 (33A40 81C12)",
MRnumber = "87j:41073",
bibdate = "Mon Oct 31 11:57:50 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v27/i11/p2738_s1",
acknowledgement = ack-nhfb,
pagecount = "10",
}
@InProceedings{Gal:1986:CEF,
author = "Shmuel Gal",
title = "Computing elementary functions: a new approach for
achieving high accuracy and good performance",
crossref = "Miranker:1986:ASC",
pages = "1--16",
year = "1986",
MRclass = "65D20",
MRnumber = "868 283",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gustavson:1986:FEF,
author = "F. G. Gustavson",
title = "Fast Elementary Function Algorithms for 370 Machines",
crossref = "Miranker:1986:ASC",
pages = "17--17",
year = "1986",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hull:1986:VPE,
author = "T. E. Hull and A. Abrham",
title = "Variable Precision Exponential Function",
journal = j-TOMS,
volume = "12",
number = "2",
pages = "79--91",
month = jun,
year = "1986",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D15 (65D20)",
MRnumber = "863 786",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/;
http://www.acm.org/pubs/toc/Abstracts/toms/6498.html",
acknowledgement = ack-nhfb,
bibno = "91",
content = "algorithms; verification; THEORY",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Algorithm analysis; G.4
Certification and testing; G.4 Verification",
CRnumber = "1986-02428",
descriptor = "mathematics of computing, numerical analysis,
approximation, elementary function approximation;
mathematics of computing, mathematical software,
algorithm analysis; mathematics of computing,
mathematical software, certification and testing;
mathematics of computing, mathematical software,
verification",
fortitle = "ACM Trans. Math. Softw.",
genterm = "June 1986",
guideno = "2",
keywords = "algorithms; theory; verification",
review = "ACM CR 8702-0091",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification.",
}
@Article{Kushner:1986:ECC,
author = "Ed Kushner and Rick Broussard",
title = "Efficient computation of the cylindrical {Bessel}
functions of complex argument",
journal = j-COMP-PHYS-COMM,
volume = "42",
number = "3",
pages = "345--349",
month = nov,
year = "1986",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(86)90004-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:16 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465586900044",
abstract = "An algorithm that generates the cylindrical Bessel
function very accurately for a wide range of complex
arguments has been developed by Mason. The Mason
algorithm consists of four different methods that apply
to different portions of the complex plane. Experience
with the Floating Point Systems FPS-364
minisupercomputer indicates several ways by which these
methods can be made more efficient. Specific
improvements relate to: (1) the method for
determination of the point where backward recursion is
initiated for the Bessel functions of the first kind;
(2) the way that the Bessel functions of the first and
second kind are normalized when $|y| < 5$ and $|x| \leq
20$; and (3) the extent that asymptotic expansions are
used when $|x| > 20$ and $|y| < 5$. The first and third
modifications will result in increased efficiency for
all architectures. The second modification will be of
value for many, but probably not all, architectures.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Lavoie:1986:SEG,
author = "J. L. Lavoie",
title = "Some evaluations for the generalized hypergeometric
series",
journal = j-MATH-COMPUT,
volume = "46",
number = "173",
pages = "215--218",
month = jan,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65D20)",
MRnumber = "87c:33007",
MRreviewer = "S. D. Bajpai",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0200 (Engineering mathematics and mathematical
techniques); B0290Z (Other numerical methods); C1100
(Mathematical techniques); C4190 (Other numerical
methods)",
corpsource = "Laval Univ., Que., Canada",
keywords = "evaluation formulae; generalized hypergeometric
series; series (mathematics); summation formulae; unit
argument; Whipple's theorem",
treatment = "T Theoretical or Mathematical",
}
@Article{Marsaglia:1986:IGF,
author = "John C. W. Marsaglia",
title = "The Incomplete Gamma Function and Ramanujan's Rational
Approximation to $\exp(x)$",
journal = "Journal of Statistical Computation and Simulation",
volume = "24",
number = "??",
pages = "163--169",
month = "????",
year = "1986",
bibdate = "Wed Jun 22 07:21:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Muller:1986:MDC,
author = "Jean-Michel Muller",
title = "Une m{\'e}thodologie du calcul hardware des fonctions
{\'e}l{\'e}mentaires. ({French}) [{A} methodology for
the hardware computation of elementary functions]",
journal = j-MATH-MODEL-NUM-ANA,
volume = "20",
number = "4",
pages = "667--695",
year = "1986",
CODEN = "RMMAEV",
ISSN = "0764-583X (print), 1290-3841 (electronic)",
MRclass = "65D20 (41-04)",
MRnumber = "88h:65043",
MRreviewer = "E. W. Cheney",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Piessens:1986:ATP,
author = "Robert Piessens and Shafique Ahmed",
title = "Approximation for the turning points of {Bessel}
functions",
journal = j-J-COMPUT-PHYS,
volume = "64",
number = "1",
pages = "253--257",
month = may,
year = "1986",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(86)90029-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:29 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199918690029X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Reichel:1986:PAU,
author = "L. Reichel",
title = "On polynomial approximation in the uniform norm by the
discrete least squares method",
journal = j-BIT,
volume = "26",
number = "3",
pages = "350--368",
month = jan,
year = "1986",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "12404",
catcode = "G.1.2; G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Least squares
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Least squares approximation; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation, Spline
and piecewise polynomial approximation",
genterm = "algorithms",
guideno = "1986-03278",
jrldate = "Jan. 1986",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{S:1986:CEF,
author = "A. S. Kuz'menko and K. I. Rogozin",
title = "Calculation of elementary functions in a number system
with arbitrary basis on the basis of order-differential
transformations. ({Russian})",
journal = "Prace Nauk. Inst. Cybernet. Tech. Politech.
Wroc{\l}aw. Ser. Konfer.",
volume = "74",
number = "31",
pages = "259--262",
year = "1986",
MRclass = "65G99 (65D20)",
MRnumber = "894 691",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Shore:1986:AID,
author = "Haim Shore",
title = "An approximation for the inverse distribution function
of a combination of random variables, with an
application to operating theatres",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "23",
number = "3",
pages = "157--181",
year = "1986",
CODEN = "JSCSAJ",
ISSN = "0094-9655 (print), 1563-5163 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Ban-llan University, Israel",
bibno = "5358",
catcode = "G.3; G.m; G.1.2; G.2.1; J.3; G.3",
content = "The author worked on a project to predict the
percentage of time that operations are carried out
relative to the time that the operating theater is
available. The numerator of the percentage is a
weighted sum of the times required to carry out
different kinds of operations, where the weights are
the numbers of operations of each kind to be performed.
Since different kinds of operations have different mean
times, this sum has a skewed distribution.\par
Based on the Central Limit Theorem, the normal
distribution is the most widely used approximation to
the distribution of a weighted sum of random variables.
However, this approximation is not very good if the sum
has a skewed distribution.\par
In a separate paper [1], the author derived an
alternative approximation based on the first four
moments of the sum. In the present paper, he applies
this approximation to the operating theater problem by
estimating the moments of the times of the different
kinds of operations. The paper also contains a Monte
Carlo comparison of the normal approximation with the
proposed approximation for four underlying
distributions of the sum.",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; G.2.1 Combinatorics;
G.2.1 Generating functions; J.3 Health; G.3
Probabilistic algorithms (including Monte Carlo)",
CRnumber = "8612-1109",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
MISCELLANEOUS; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions;
Computer Applications, LIFE AND MEDICAL SCIENCES,
Health; Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo)",
genterm = "algorithms; measurement",
journalabbrev = "J. Stat. Comput. Simul.",
jrldate = "1986",
reviewer = "M. Snyder",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.m
MISCELLANEOUS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
DISCRETE MATHEMATICS; J. Computer Applications; J.3
LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing;
G.3 PROBABILITY AND STATISTICS",
}
@Article{Skeel:1986:CVS,
author = "Robert D. Skeel",
title = "Construction of Variable-Stepsize Multistep Formulas",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "503--510, S45--S52",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65L05",
MRnumber = "87j:65080",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4110 (Error analysis in numerical methods); C4170
(Differential equations)",
corpsource = "Dept. of Comput. Sci., Illnois Univ., Urbana, IL,
USA",
keywords = "Adams formula; adaptable multistep methods;
backward-differentiation; differential equations; error
analysis; estimation; first Dahlquist barrier; fixed
leading coefficient method; fixed-coefficient methods;
fixed-stepsize; formula; formula changing; initial
value; interpolatory methods; local error; minimum
storage variable-stepsize; multistep formula; Nordsieck
stepsize changing technique; problems; step methods;
variable; variable coefficient methods; variable-order
family of variable-coefficient formulas",
treatment = "T Theoretical or Mathematical",
}
@Article{Skeel:1986:SCV,
author = "Robert D. Skeel",
title = "Supplement to Construction of Variable-Stepsize
Multistep Formulas",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "S45--S52",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Temme:1986:DIC,
author = "N. M. Temme",
title = "A double integral containing the modified {Bessel}
function: asymptotics and computation",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "683--691",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A40 (41A60 65D30)",
MRnumber = "87m:33006",
MRreviewer = "S. D. Bajpai",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4110 (Error analysis in numerical methods); C4130
(Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Centre for Math. and Comput. Sci., Amsterdam,
Netherlands",
keywords = "distribution function; double integral; error
analysis; error function; integral; integration;
modified Bessel function; normal; polynomials;
probability; series (mathematics); series expansions;
two-dimensional",
treatment = "T Theoretical or Mathematical",
}
@Article{Thompson:1986:CBF,
author = "I. J. Thompson and A. R. Barnett",
title = "{Coulomb} and {Bessel} functions of complex arguments
and order",
journal = j-J-COMPUT-PHYS,
volume = "64",
number = "2",
pages = "490--509",
month = jun,
year = "1986",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(86)90046-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:30 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199918690046X",
abstract = "The Coulomb wavefunctions, originally constructed for
real $\varrho > 0$, real $\eta$ and integer $\lambda
\geq 0$ are defined for $\varrho$, $\eta$, and
$\lambda$ all complex. We examine the complex
continuation of a variety of series and
continued-fraction expansions for the Coulomb functions
and their logarithmic derivatives, and then see how
these expansions may be selectively combined to
calculate both the regular and irregular functions and
their derivatives. The resulting algorithm [46] is a
complex generalisation of Steed's method [6, 7] as it
appears in the real procedure COULFG [10]. Complex
Whittaker, confluent hypergeometric and Bessel
functions can also be calculated.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Zaritskaya:1986:ACE,
author = "Z. V. Zaritskaya and A. I. Shva{\u{\i}} and P. \=E.
Antonyuk",
title = "Approximation of certain elementary functions in the
metric ${L}$. ({Russian})",
journal = "Vestnik L'vov. Politekhn. Inst.",
volume = "202",
pages = "38--40",
year = "1986",
MRclass = "149.41A10 (33A10)",
MRnumber = "87j:41030",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Agarwal:1987:CNS,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "Clarification: {``New scalar and vector elementary
functions for the IBM System/370''} [{IBM J. Res.
Develop. {\bf 30} (1986), no. 2, 126--144}]",
journal = j-IBM-JRD,
volume = "31",
number = "2",
pages = "274--274",
year = "1987",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "76W05",
MRnumber = "MR894626",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Agarwal:1986:NSV}.",
acknowledgement = ack-nhfb,
fjournal = "International Business Machines Corporation. Journal
of Research and Development",
}
@PhdThesis{Braune:1987:HSF,
author = "K. Braune",
title = "{Hochgenaue Standardfunktionen f{\"u}r reelle und
komplexe Punkte und Intervalle in beliebigen
Gleitpunktrastern} \toenglish {High-Accuracy Elementary
Functions for Real and Complex Points and Intervals in
Arbitrary Floating-Point Systems} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1987",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Buhring:1987:BUA,
author = "Wolfgang B{\"u}hring",
title = "The behavior at unit argument of the hypergeometric
function {${}_3F_2$}",
journal = j-SIAM-J-MATH-ANA,
volume = "18",
number = "5",
pages = "1227--1234",
month = sep,
year = "1987",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "88j:33004",
MRreviewer = "K. M. Saksena",
bibdate = "Sun Nov 28 19:24:11 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/5;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Article{Carlson:1987:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals of the Second Kind",
journal = j-MATH-COMPUT,
volume = "49",
number = "180",
pages = "595--606, S13--S17",
month = oct,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (33A25 65V05)",
MRnumber = "89b:65013",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4160 (Numerical integration and differentiation);
C7310 (Mathematics)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
keywords = "elliptic integrals of the second kind; FORTRAN
listings; integration; mathematics computing; standard
R-functions",
treatment = "P Practical; T Theoretical or Mathematical; X
Experimental",
}
@Article{Crandall:1987:EFE,
author = "R. E. Crandall and J. P. Buhler",
title = "Elementary function expansions for {Madelung}
constants",
journal = j-J-PHYS-A,
volume = "20",
number = "16",
pages = "5497--5510",
year = "1987",
CODEN = "JPHAC5",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
MRclass = "82A60 (82-08)",
MRnumber = "MR924725 (88m:82034)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics. A. Mathematical and General",
}
@Article{Dunham:1987:PMAa,
author = "Charles B. Dunham",
title = "Provably monotone approximations",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "6--11",
month = apr,
year = "1987",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/24936.24938",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:15 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "theory; verification",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Dunham:1987:PMAb,
author = "Charles B. Dunham",
title = "Provably monotone approximations, {II}",
journal = j-SIGNUM,
volume = "22",
number = "3",
pages = "30--31",
month = jul,
year = "1987",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/36318.36323",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:15 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Gervais:1987:RAF,
author = "R. Gervais and Q. I. Rahman and G. Schmeisser",
title = "Representation and approximation of functions via
$(0,2)$-interpolation",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "2",
pages = "89--110",
month = jun,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30719",
catcode = "G.1.2; G.1.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation",
genterm = "theory; verification",
guideno = "1987-09238",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Johnson:1987:AES,
author = "Kenneth C. Johnson",
title = "{Algorithm 650}: Efficient Square Root Implementation
on the 68000",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "138--151",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/328512.328520",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "898 489",
bibdate = "Sun Sep 4 21:36:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also \cite{Johnson:1987:CES}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
}
@Article{Johnson:1987:CES,
author = "Kenneth C. Johnson",
title = "Corrigendum: {``Algorithm 650: efficient square root
implementation on the 68000'' [{ACM} Trans. Math.
Software {\bf 13} (1987), no. 2, 138--151]}",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "320--320",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/29380.356210",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "320. 65D15",
MRnumber = "918 582",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Johnson:1987:AES}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
}
@InProceedings{Kahan:1987:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions or Much
Ado About Nothing's Sign Bit",
crossref = "Iserles:1987:SAN",
volume = "9",
pages = "165--211",
year = "1987",
MRclass = "65E05",
MRnumber = "88k:65027",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
acknowledgement = ack-nhfb,
}
@PhdThesis{Kramer:1987:ISR,
author = "W. Kr{\"a}mer",
title = "Inverse Standardfunktionen f{\"u}r reelle und komplexe
Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
f{\"u}r beliebige Datenformate \toenglish {Inverse
Elementary Functions for Real and Complex Interval
Arguments with {A}-Priori Error Estimates for Arbitrary
Data Formats} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1987",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Lewanowicz:1987:CRR,
author = "Stanis{\l}aw Lewanowicz",
title = "Corrigendum: {``Recurrence relations for
hypergeometric functions of unit argument''} {[Math.
Comp. {\bf 45} (1985), no. 172, 521--535, MR
86m:33004]}",
journal = j-MATH-COMPUT,
volume = "48",
number = "178",
pages = "853--853",
month = apr,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65Q05)",
MRnumber = "88a:33013",
bibdate = "Wed Jan 15 09:19:34 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Liu:1987:BEF,
author = "Z. A. Liu",
title = "{Berkeley} Elementary Function Test Suite",
type = "{M.S.} thesis",
school = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
month = dec,
year = "1987",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
}
@Article{Lo:1987:HGA,
author = "Hao-Yung Lo and Jau-Ling Chen",
title = "A Hardwired Generalized Algorithm for Generating the
Logarithm Base-$k$ by Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1363--1367",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1987.5009477",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:57 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009477",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@InProceedings{Mathis:1987:EFP,
author = "Robert F. Mathis",
title = "Elementary Functions Package for {Ada}",
crossref = "ACM:1987:UAA",
pages = "95--100",
month = dec,
year = "1987",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Moricz:1987:ACF,
author = "Ferenc Moricz and Xianliang Shi",
title = "Approximation to continuous functions by {Cesaro}
means of double {Fourier} series and conjugate series",
journal = j-J-APPROX-THEORY,
volume = "49",
number = "4",
pages = "346--377",
month = apr,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30744",
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Least squares
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Least squares approximation",
genterm = "theory; verification",
guideno = "1987-09224",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Musielak:1987:AEG,
author = "J. Musielak",
title = "Approximation of elements of a generalized {Orlicz}
sequence space by nonlinear, singular kernels",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "4",
pages = "366--372",
month = aug,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30716",
catcode = "G.2.1; G.1.5; G.1.2",
CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5
Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Generating functions; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Convergence; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory; verification",
guideno = "1987-09257",
journalabbrev = "J. Approx. Theory",
jrldate = "Aug. 1987",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Pereira:1987:CEC,
author = "N. Costa Pereira",
title = "Corrigendum: {``Estimates for the {Chebyshev} function
$\psi(x) - \theta(x)$''} {[Math. Comp. {\bf 44} (1985),
no. 169, 211--221, MR 86k:11005]}",
journal = j-MATH-COMPUT,
volume = "48",
number = "177",
pages = "447--447",
month = jan,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11A25 (11N45 11Y35 33A70)",
MRnumber = "87k:11006",
bibdate = "Thu Jun 15 07:27:03 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Pereira:1985:ECF}.",
acknowledgement = ack-nhfb,
}
@Article{Proinov:1987:NIA,
author = "Petko D. Proinov",
title = "Numerical integration and approximation of
differentiable functions, {II}",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "4",
pages = "373--393",
month = aug,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30717",
catcode = "G.1.4; G.1.2",
CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "theory; verification",
guideno = "1987-09258",
journalabbrev = "J. Approx. Theory",
jrldate = "Aug. 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Rolfe:1987:FIS,
author = "Timothy J. Rolfe",
title = "On a Fast Integer Square Root Algorithm",
journal = j-SIGNUM,
volume = "22",
number = "4",
pages = "6--11",
month = oct,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
keywords = "algorithms; performance; theory",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations",
}
@Article{Smith:1987:BAM,
author = "P. W. Smith and J. J. Swetits",
title = "Best approximation by monotone functions",
journal = j-J-APPROX-THEORY,
volume = "49",
number = "4",
pages = "398--403",
month = apr,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30747",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory; verification",
guideno = "1987-09227",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Spanier:1987:AF,
author = "Jerome Spanier and Keith B. Oldham",
title = "An Atlas of Functions",
publisher = "Hemisphere Publishing Corporation",
address = "Washington, DC, USA",
pages = "ix + 700",
year = "1987",
ISBN = "0-89116-573-8, 3-540-17395-1",
ISBN-13 = "978-0-89116-573-6, 978-3-540-17395-3",
LCCN = "QA331 .S685 1987",
bibdate = "Fri Aug 31 16:20:13 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90.00 (est.)",
acknowledgement = ack-nhfb,
subject = "elementary functions; special functions; cognate
functions; complementary incomplete gamma function;
complementary modulus; complete beta function; complex
argument when; cosecant functions; cotangent functions;
digamma function; economized polynomial; error function
complement; eta numbers; function and its reciprocal;
hypergeometric algorithm; important definite integrals;
incomplete elliptic integrals; inverse gudermannian
function; inverse hyperbolic functions; negative
integer order; other definite integrals; parabolic
cylinder function; polygamma functions; purely
imaginary argument; reciprocal linear function;
reflection formula",
}
@Article{Stoyanov:1987:AE,
author = "Basil J. Stoyanov and Richard A. Farrell",
title = "On the Asymptotic Evaluation of $\int^{\pi/2}_0
{J}^2_0(\gamma \sin x) dx$",
journal = j-MATH-COMPUT,
volume = "49",
number = "179",
pages = "275--279",
month = jul,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "41A60 (65D30)",
MRnumber = "88e:41067",
MRreviewer = "Roderick Wong",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1120 (Analysis); C4180 (Integral equations)",
corpsource = "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD,
USA",
keywords = "analytical expression; asymptotic behavior; asymptotic
evaluation; Bessel functions; first kind; integral;
integral equations; order Bessel function; positive
parameter; zeroth-",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Tanese:1987:PGA,
author = "Reiko Tanese",
editor = "John J. Grefenstette",
booktitle = "Genetic algorithms and their applications: proceedings
of the second International Conference on Genetic
Algorithms: July 28--31, 1987 at the Massachusetts
Institute of Technology, Cambridge, MA",
title = "Parallel genetic algorithms for a hypercube",
publisher = pub-ERLBAUM,
address = pub-ERLBAUM:adr,
pages = "177--183",
year = "1987",
ISBN = "0-8058-0158-8, 0-8058-0159-6 (paperback)",
ISBN-13 = "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)",
LCCN = "Q334 .I5561 1987",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$39.95",
acknowledgement = ack-nhfb,
bibno = "42536",
bookpages = "260",
catcode = "I.2.6; G.1.0; G.1.2; C.1.2",
CRclass = "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0
Parallel algorithms; G.1.2 Approximation; G.1.2
Elementary function approximation; C.1.2 Multiple Data
Stream Architectures (Multiprocessors); C.1.2 Parallel
processors",
descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Learning, Analogies; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Parallel algorithms;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Parallel processors",
genterm = "algorithms; performance; experimentation",
guideno = "1988-16888",
procdate = "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and
Bolt Beranek & Newman, July 28-31, 1987",
procloc = "Cambridge, MA",
subject = "I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
}
@Article{Thompson:1987:IEF,
author = "Peter Thompson",
title = "Implementing an Elementary Function Library",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "2--5",
month = apr,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
bibno = "24937",
catcode = "G.m; D.3.2",
CRclass = "D.3.2 Language Classifications; D.3.2 OCCAM",
descriptor = "Mathematics of Computing, MISCELLANEOUS; Software,
PROGRAMMING LANGUAGES, Language Classifications,
OCCAM",
genterm = "theory; languages",
guideno = "1987-03363",
journalabbrev = "SIGNUM Newsl.",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.m MISCELLANEOUS; D.
Software; D.3 PROGRAMMING LANGUAGES",
}
@Article{Thompson:1987:MBF,
author = "I. J. Thompson and A. R. Barnett",
title = "Modified {Bessel} functions {$I_\nu(z)$} and
{$K_\nu(z)$} of real order and complex argument, to
selected accuracy",
journal = j-COMP-PHYS-COMM,
volume = "47",
number = "2--3",
pages = "245--257",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(87)90111-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:21 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
note = "See erratum \cite{Thompson:2004:EBB}.",
URL = "http://www.sciencedirect.com/science/article/pii/0010465587901111",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Timan:1987:DFP,
author = "A. F. Timan",
title = "Distribution of fractional parts and approximation of
functions with singularities by {Bernstein}
polynomials",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "2",
pages = "167--174",
month = jun,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30725",
catcode = "G.1.5; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials,
methods for; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Polynomials, methods for;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory; verification",
guideno = "1987-09244",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Visentin:1987:FAE,
author = "Kley Visentin and Pablo Mart{\'\i}n",
title = "Fractional approximation to elliptic functions",
journal = j-J-MATH-PHYS,
volume = "28",
number = "2",
pages = "330--333",
month = feb,
year = "1987",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.527661",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A10 (33A65)",
MRnumber = "87m:41009",
bibdate = "Mon Oct 31 11:57:55 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v28/i2/p330_s1",
acknowledgement = ack-nhfb,
pagecount = "4",
}
@Article{Zurawski:1987:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of a High-Speed Square Root Multiply and Divide
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "13--23",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1987.5009445",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Zwick:1987:BAC,
author = "D. Zwick",
title = "Best approximation by convex functions",
journal = j-AMER-MATH-MONTHLY,
volume = "94",
number = "6",
pages = "528--534",
month = jul,
year = "1987",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "University of Vermont, Vermont, NY",
bibno = "43727",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory; verification",
guideno = "1988-04405",
journalabbrev = "Am. Math. Monthly",
jrldate = "June/July 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Aberth:1988:PNA,
author = "Oliver Aberth",
title = "Precise Numerical Analysis",
publisher = pub-WCB,
address = pub-WCB:adr,
pages = "x + 225",
year = "1988",
ISBN = "0-697-06760-2",
ISBN-13 = "978-0-697-06760-9",
LCCN = "QA297 .A28 1988",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Aberth addresses elementary issues of precise floating
point computations using variable precision range
arithmetic. Numbers are represented as a variable
precision number $\pm$ a range. Rational arithmetic is
also considered. Chapters are devoted to
\begin{enumerate} \item rootfinding, \item polynomial
rootfinding, \item numerical linear algebra, \item
differentiation and integration, and \item ordinary
differential equations.\end{enumerate} Differentiation
is handled by a codelist approach like [Rall81a], and
applications to Taylor series are given. Interval
techniques for ordinary differential equations are
based on using an {\it a priori\/} bound to capture
remainder terms. Several methods are illustrated,
including Taylor series methods.",
acknowledgement = ack-nj,
comment = "Text for a one semester, junior level course in
numerical analysis. Includes PC disk with software
written in PBASIC. Sound introductory level discussion
of code lists and error capture techniques.",
keywords = "differentiation; differentiation arithmetic; general
numerical analysis; integration; interval techniques;
linear algebra; ordinary differential equations.;
variable precision arithmetic",
}
@Article{Alonso:1988:SCN,
author = "Javier Alonso and Carlos Benitez",
title = "Some characteristic and non-characteristic properties
of inner product spaces",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "318--325",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56052",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "theory; verification",
guideno = "1988-10198",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Bailey:1988:CDD,
author = "David H. Bailey",
title = "The computation of $\pi$ to $29,360,000$ decimal
digits using {Borweins}' quartically convergent
algorithm",
journal = j-MATH-COMPUT,
volume = "50",
number = "181",
pages = "283--296",
month = jan,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11Y60 (11-04 11K16 65-04)",
MRnumber = "88m:11114",
MRreviewer = "A. J. van der Poorten",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1140Z (Other and miscellaneous); C1160 (Combinatorial
mathematics); C4130 (Interpolation and function
approximation); C5470 (Performance evaluation and
testing); C7310 (Mathematics)",
corpsource = "NASA Ames Res. Centre, Moffet Field, CA, USA",
keywords = "Borwein quartically convergent algorithm; computation
of pi; computer testing; Cray 2 computer test; decimal
expansion; elliptic integrals; iterative methods;
mathematics computing; multiprecision arithmetic;
number theory; prime modulus; series (mathematics);
statistical analyses; statistical analysis; transform",
treatment = "X Experimental",
}
@Article{Bloom:1988:LCL,
author = "Thomas Bloom",
title = "The {Lebesgue} constant for {Lagrange} interpolation
in the simplex",
journal = j-J-APPROX-THEORY,
volume = "54",
number = "3",
pages = "338--353",
month = sep,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56887",
catcode = "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7",
CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas;
G.1.2 Approximation; G.1.2 Minimax approximation and
algorithms; G.1.2 Approximation; G.1.2 Elementary
function approximation; G.1.7 Ordinary Differential
Equations; G.1.7 Convergence and stability; G.1.7
Ordinary Differential Equations; G.1.7 Boundary value
problems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Interpolation formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Convergence
and stability; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems",
guideno = "1988-10170",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Borwein:1988:CFF,
author = "J. M. Borwein and P. B. Borwein",
title = "On the complexity of familiar functions and numbers",
journal = j-SIAM-REVIEW,
volume = "30",
number = "4",
pages = "589--601",
month = dec,
year = "1988",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58008",
catcode = "G.1.2; F.2.1; F.1.3",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; F.2.1 Numerical Algorithms and Problems;
F.1.3 Complexity Classes",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes",
genterm = "algorithms; theory; performance",
guideno = "1988-13907",
journalabbrev = "SIAM Rev.",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1
COMPUTATION BY ABSTRACT DEVICES",
}
@Article{Borwein:1988:PAE,
author = "Peter B. Borwein",
title = "{Pad{\'e}} approximants for the $q$-elementary
functions",
journal = j-CONST-APPROX,
volume = "4",
number = "4",
pages = "391--402",
year = "1988",
ISSN = "0176-4276",
MRclass = "41A21 (33A10 41A20)",
MRnumber = "89f:41022",
MRreviewer = "Annie A. M. Cuyt",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Brezinski:1988:NAC,
author = "Claude Brezinski",
booktitle = "{Nonlinear numerical methods and rational
approximation (Wilrijk, 1987)}",
title = "A new approach to convergence acceleration methods",
volume = "43",
publisher = "Reidel",
address = "Dordrecht",
pages = "373--405",
year = "1988",
MRclass = "65Bxx (40A25)",
MRnumber = "1005369 (90m:65010)",
MRreviewer = "John P. Coleman",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Math. Appl.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Carlson:1988:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals of the Third Kind",
journal = j-MATH-COMPUT,
volume = "51",
number = "183",
pages = "267--280, S1--S5",
month = jul,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33A25 (65A05)",
MRnumber = "89k:33003",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); B0220 (Analysis); B0290D
(Functional analysis); B0290M (Numerical integration
and differentiation); C4180 (Integral equations); C1120
(Analysis); C4120 (Functional analysis); C4160
(Numerical integration and differentiation)",
corpsource = "Iowa State Univ., Ames, IA, USA",
keywords = "Cauchy principal values; elliptic integrals; FORTRAN
listings; function evaluation; integral equations;
integration; points; real singular; recurrence
relations; standard R-functions",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Cartwright:1988:JTC,
author = "Donald I. Cartwright and Krzysztof Kucharski",
title = "{Jackson's Theorem} for compact connect {Lie} groups",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "352--359",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56056",
catcode = "G.2.m; G.1.2",
CRclass = "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "verification; theory",
guideno = "1988-10202",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Chiccoli:1988:EGE,
author = "C. Chiccoli and S. Lorenzutta and G. Maino",
title = "On the evaluation of generalized exponential integrals
{$E_\nu(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "78",
number = "2",
pages = "278--287",
month = oct,
year = "1988",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(88)90050-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:42 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188900502",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Cover:1988:DII,
author = "Thomas M. Cover and Joy A. Thomas",
title = "Determinant inequalities via information theory",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "9",
number = "3",
pages = "384--392",
month = jul,
year = "1988",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58040",
catcode = "H.1.1; G.1.3; F.2.1; G.1.2",
CRclass = "H.1.1 Systems and Information Theory; H.1.1
Information theory; G.1.3 Numerical Linear Algebra;
G.1.3 Determinants; F.2.1 Numerical Algorithms and
Problems; F.2.1 Computations on matrices; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Information Systems, MODELS AND PRINCIPLES, Systems
and Information Theory, Information theory; Mathematics
of Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Determinants; Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; theory; performance",
guideno = "1988-13777",
journalabbrev = "SIAM J. Matrix Anal. Appl.",
jrldate = "July 1988",
subject = "H. Information Systems; H.1 MODELS AND PRINCIPLES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@InProceedings{Davenport:1988:ICF,
author = "J. H. Davenport",
editor = "N. M. Stephens and M. P. Thorne",
booktitle = "Computers in mathematical research: based on the
proceedings of a conference organized by the Institute
of Mathematics and its Applications on computers in
mathematical research, held at University College,
Cardiff in September 1986",
title = "Integration in closed form",
volume = "14",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
year = "1988",
ISBN = "0-19-853620-8",
ISBN-13 = "978-0-19-853620-8",
LCCN = "QA11.A1 C618 1986",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$57.50",
series = "Institute of Mathematics and its applications
conference series, new series",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Bath",
bibno = "52474",
bookpages = "235",
catcode = "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1",
CRclass = "J.2 Mathematics and statistics; F.2.1 Numerical
Algorithms and Problems; F.2.1 Number-theoretic
computations; G.1.2 Approximation; G.1.2 Rational
approximation; G.1.2 Approximation; G.1.2 Elementary
function approximation; I.2.9 Robotics; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations in finite
fields",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Robotics; Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations in finite
fields",
genterm = "algorithms; theory",
guideno = "1988-16247",
page = "119--134",
procdate = "Sept. 1986",
procloc = "Cardiff, Wales",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; I. Computing
Methodologies; I.2 ARTIFICIAL INTELLIGENCE; F. Theory
of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY",
waffil = "Univ. College, Cardiff, Wales; Univ. College, Cardiff,
Wales",
}
@Article{Dunham:1988:PMA,
author = "Charles B. Dunham",
title = "Provably monotone approximations, {III}",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "10--10",
month = jan,
year = "1988",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/43931.43934",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@TechReport{Duprat:1988:EPE,
author = "J. Duprat and J. M. Muller",
title = "Evaluation of Polynomials and elementary Functions by
integrated Circuits",
number = "RR698-I",
institution = "IMAG",
address = "Grenoble, France",
month = jan,
year = "1988",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Duprat:1988:HPE,
author = "Jean Duprat and Jean-Michel Muller",
title = "Hardwired polynomial evaluation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "291--309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "CNRS, Grenoble, Fr",
classification = "721; 722; 723; 921; C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
corpsource = "Inst. Nat. Polytech. de Grenoble, France",
journalabr = "J Parallel Distrib Comput",
keywords = "computer architecture; computers, digital ---
Circuits; digital arithmetic; elementary functions;
hardwired polynomial evaluation; mathematical
functions; mathematical techniques; Polynomials;
polynomials; special-purpose circuits; VLSI
implementation",
treatment = "P Practical",
}
@Article{Feng:1988:AIN,
author = "Y. Y. Feng and J. Kozak",
title = "An approach to the interpolation of nonuniformly
spaced data",
journal = j-J-COMP-APPL-MATH,
volume = "23",
number = "2",
pages = "169--178",
month = aug,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56475",
catcode = "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4",
CRclass = "G.1.1 Interpolation; G.1.1 Spline and piecewise
polynomial interpolation; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.7 Ordinary
Differential Equations; G.1.7 Boundary value problems;
G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature
and Numerical Differentiation; G.1.4 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Smoothing; Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Error analysis",
genterm = "algorithms; theory",
guideno = "1988-10490",
journalabbrev = "J. Comput. Appl. Math.",
jrldate = "August 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Gawronski:1988:ZLT,
author = "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller",
title = "On the zeros of {Lerch}'s transcendental function of
real parameters",
journal = j-J-APPROX-THEORY,
volume = "53",
number = "3",
pages = "354--364",
month = jun,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG",
bibno = "49727",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1988-10146",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Guerrero:1988:HOT,
author = "Antonio L. Guerrero and Pablo Martin",
title = "Higher order two-point quasi-fractional approximations
to the {Bessel} functions {$J_0(x)$} and {$J_1(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "77",
number = "1",
pages = "276--281",
month = jul,
year = "1988",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(88)90168-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:41 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188901684",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
remark = "This work produces only 3D approximations.",
}
@Article{Hautot:1988:CAC,
author = "A. Hautot",
title = "Convergence acceleration of continued fractions of
{Poincar{\'e}} type",
journal = j-APPL-NUM-MATH,
volume = "4",
number = "2--4",
pages = "309--322",
month = jun,
year = "1988",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "65B05 (40A15)",
MRnumber = "90b:65005",
MRreviewer = "Gh. Adam",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Heilmann:1988:SSM,
author = "Margareta Heilmann",
title = "{$L_p$}-saturation of some modified {Bernstein}
operators",
journal = j-J-APPROX-THEORY,
volume = "54",
number = "3",
pages = "260--273",
month = sep,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56880",
catcode = "G.1.2; G.1.9; G.1.7; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.9 Integral Equations; G.1.9
Integro-differential equations; G.1.7 Ordinary
Differential Equations; G.1.7 Boundary value problems;
G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Mathematics
of Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Boundary value problems; Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Convergence and stability",
genterm = "algorithms; theory",
guideno = "1988-10163",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Horwitz:1988:TPF,
author = "Alan L. Horwitz and Lee A. Rubel",
title = "Totally positive functions and totally bounded
functions on $[-1,1]$",
journal = j-J-APPROX-THEORY,
volume = "52",
number = "2",
pages = "204--216",
month = feb,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ., University Park; Univ. of
Illinois, Urbana",
bibno = "49653",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1988-10106",
journalabbrev = "J. Approx. Theory",
jrldate = "February 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Jacobsen:1988:CAL,
author = "Lisa Jacobsen and Haakon Waadeland",
title = "Convergence acceleration of limit periodic continued
fractions under asymptotic side conditions",
journal = j-NUM-MATH,
volume = "53",
number = "3",
pages = "285--298",
month = jul,
year = "1988",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
MRclass = "65B99 (30B70 40A15)",
MRnumber = "89h:65010",
MRreviewer = "Claude Brezinski",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Dept. of Math. and Stat., Trondheim Univ., Dragvoll,
Norway",
keywords = "asymptotic side conditions; convergence acceleration;
convergence of numerical methods; hypergeometric
functions; limit periodic continued fractions; regular
C-fraction expansions",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Johnsson:1988:DPP,
author = "S. L. Johnsson",
editor = "J. R. Rice",
booktitle = "Mathematical aspects of scientific software",
title = "Data parallel programming and basic linear algebra
subroutines",
volume = "14",
publisher = pub-SV,
address = pub-SV:adr,
pages = "183--196",
year = "1988",
ISBN = "0-387-96706-0",
ISBN-13 = "978-0-387-96706-6",
LCCN = "QA76.76.D47 M366 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "The IMS volumes in mathematics and its applications",
acknowledgement = ack-nhfb,
bibno = "42725",
bookpages = "vi + 208",
catcode = "G.1.2; D.1.m; G.4",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; D.1.m Miscellaneous",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Software, PROGRAMMING TECHNIQUES, Miscellaneous;
Mathematics of Computing, MATHEMATICAL SOFTWARE",
genterm = "theory; algorithms; design; languages",
guideno = "1988-02324",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics
of Computing; G.4 MATHEMATICAL SOFTWARE",
waffil = "Purdue Univ., West Lafayette, IN",
}
@Article{Kowalski:1988:ASP,
author = "Marek Kowalski and Waldemar Sielski",
title = "Approximation of smooth periodic functions in several
variables",
journal = j-J-COMPLEXITY,
volume = "4",
number = "4",
pages = "356--372",
month = dec,
year = "1988",
CODEN = "JOCOEH",
ISSN = "0885-064X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56811",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; verification; theory",
guideno = "1988-10411",
journalabbrev = "J. Complexity",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Kramer:1988:ISF,
author = "W. Kramer",
title = "Inverse standard functions for real and complex point
and interval arguments with dynamic accuracy",
journal = j-COMPUTING-SUPPLEMENTUM,
pages = "185--212",
year = "1988",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibdate = "Thu Dec 14 17:19:38 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Computer Arithmetic and Scientific Computation.",
abstract = "Algorithms to compute inverse standard functions to
arbitrary accuracy with safe error bounds are given.
Not only approximation errors but also all possible
rounding errors are considered. The desired accuracy of
the function as well as the base of the number system
used are parameters of the error formula. For
implementation it is only assumed that the four
elementary arithmetic operations are performed with a
certain number of correct digits of the function value.
The interval routines are constructed out of the point
routines considering the monotonicity behaviour of the
functions. The ambiguity of the complex functions is
briefly discussed.",
acknowledgement = ack-nhfb,
affiliation = "Karlsruhe Univ., West Germany",
classification = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
confdate = "30 Sept.-2 Oct. 1987",
conflocation = "Karlsruhe, West Germany",
confsponsor = "Karlsruhe Univ.; GAMM Committee",
issue = "no.6 p. 185-212",
keywords = "Approximation errors; Dynamic accuracy; Error formula;
Interval arguments; Inverse standard functions;
Monotonicity behaviour; Rounding errors",
language = "English",
pubcountry = "Austria",
thesaurus = "Error analysis; Function approximation",
}
@Article{Lembarki:1988:CAL,
author = "Alami Lembarki",
title = "Convergence acceleration of limit $k$-periodic
continued fractions",
journal = j-APPL-NUM-MATH,
volume = "4",
number = "2--4",
pages = "337--349",
month = jun,
year = "1988",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "65B05 (40A15)",
MRnumber = "89j:65012",
MRreviewer = "Thomas A. Atchison",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InCollection{Levrie:1988:CAM,
author = "Paul Levrie and Robert Piessens",
booktitle = "{Nonlinear numerical methods and rational
approximation (Wilrijk, 1987)}",
title = "Convergence acceleration for {Miller}'s algorithm",
volume = "43",
publisher = "Reidel",
address = "Dordrecht, The Netherlands",
pages = "349--370",
year = "1988",
MRclass = "65B10 (26C15 39A10)",
MRnumber = "1005368 (90m:65012)",
MRreviewer = "Pierre Hillion",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Math. Appl.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Lou:1988:ETR,
author = "Lou van den Dries",
title = "On the elementary theory of restricted elementary
functions",
journal = j-J-SYMBOLIC-LOGIC,
volume = "53",
number = "3",
pages = "796--808",
year = "1988",
CODEN = "JSYLA6",
ISSN = "0022-4812",
MRclass = "03C65 (03C40 03C68 12L12)",
MRnumber = "89i:03074",
MRreviewer = "M. Yasuhara",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Marsaglia:1988:CES,
author = "John Christopher Winston Marsaglia",
title = "Computer Evaluation of the special functions of
probability and statistics",
type = "{Ph.D.} Dissertation",
school = "Department of Computer Science, Washington State
University",
address = "Pullman, WA, USA",
pages = "vii + 79",
month = aug,
year = "1988",
bibdate = "Wed Jun 22 07:17:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "$\exp(x)$; $\Phi(x)$; Bernoulli numbers; chi-square
distribution; continued fraction; continuous Poisson
distribution; Erlang distribution; exponential
distribution; Gamma function; incomplete Gamma
function; normal distribution; normal probability
distribution; Poisson distribution; Stirling's
approximation",
}
@Article{Mimachi:1988:PRI,
author = "Katsuhisa Mimachi",
title = "A proof of {Ramanujan}'s identity by use of loop
integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "19",
number = "6",
pages = "1490--1493",
month = nov,
year = "1988",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58904",
catcode = "G.1.9; G.1.2; F.2.2",
CRclass = "G.1.9 Integral Equations; G.1.9 Integro-differential
equations; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
genterm = "algorithms; theory",
guideno = "1988-13744",
journalabbrev = "SIAM J. Math. Anal.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY",
}
@Book{Nikiforov:1988:SFM,
author = "Arnol'd F. Nikiforov and Vasilij B. Uvarov",
title = "Special functions of mathematical physics: a unified
introduction with applications",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xviii + 427",
year = "1988",
ISBN = "3-7643-3183-6, 0-8176-3183-6",
ISBN-13 = "978-3-7643-3183-2, 978-0-8176-3183-3",
LCCN = "QC20.7.F87 N692e",
bibdate = "Sat Oct 30 18:34:41 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.gbv.de:20011/gvk",
note = "Translated from the Russian by Ralph P. Boas.",
URL = "http://www.gbv.de/dms/hbz/toc/ht002696178",
acknowledgement = ack-nhfb,
}
@Article{Olver:1988:EBL,
author = "F. W. J. Olver",
title = "Error Bounds for Linear Recurrence Relations",
journal = j-MATH-COMPUT,
volume = "50",
number = "182",
pages = "481--499",
month = apr,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65Q05 (39A10 65G05)",
MRnumber = "89e:65146",
MRreviewer = "B. Choczewski",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Maryland Univ., College Park, MD, USA",
keywords = "a posteriori methods; analysis; Bessel function;
bounds; computational complexity; difference equations;
error; homogeneous second order; Legendre function;
linear recurrence relations; monotonic systems;
numerical examples; O(r) arithmetic operations;
oscillatory systems; realistic error; relations;
rounded interval arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Polyak:1988:SOM,
author = "R. A. Polyak",
title = "Smooth optimization methods for minimax problems",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "26",
number = "6",
pages = "1274--1286",
month = nov,
year = "1988",
CODEN = "SJCODC",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "57989",
catcode = "G.1.6; G.1.2; F.2.1; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2
Approximation; G.1.2 Minimax approximation and
algorithms; F.2.1 Numerical Algorithms and Problems;
F.2.1 Computation of transforms; G.1.2 Approximation;
G.1.2 Elementary function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Nonlinear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computation of
transforms; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; theory; performance",
guideno = "1988-13621",
journalabbrev = "SIAM J. Control Optim.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@InCollection{Powell:1988:RBF,
author = "J. D. Powell",
editor = "D. F. (David Francis) Griffiths and G. A. Watson",
booktitle = "Numerical analysis 1987",
title = "Radial basis function approximations to polynomials",
volume = "170",
publisher = "Longman, Inc.",
address = "New York, NY, USA",
pages = "223--241",
year = "1988",
ISBN = "0-582-02157-X",
ISBN-13 = "978-0-582-02157-0",
LCCN = "QA297.N828 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$54.95",
series = "Pitman research notes in mathematics series",
acknowledgement = ack-nhfb,
bibno = "54996",
bookpages = "300",
catcode = "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation; G.1.9 Integral
Equations; G.1.9 Integro-differential equations; G.1.1
Interpolation; G.1.1 Spline and piecewise polynomial
interpolation; G.3 Statistical computing; G.1.7
Ordinary Differential Equations; G.1.7 Convergence and
stability",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations, Integro-differential
equations; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Spline and piecewise
polynomial interpolation; Mathematics of Computing,
PROBABILITY AND STATISTICS, Statistical computing;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability",
genterm = "algorithms; performance",
guideno = "1988-01246",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.3 PROBABILITY AND STATISTICS",
waffil = "Univ. of Dundee; Univ. of Dundee",
}
@Article{Proinov:1988:ISF,
author = "Petko D. Proinov",
title = "Integration of smooth functions and
$\phi$-discrepancy",
journal = j-J-APPROX-THEORY,
volume = "52",
number = "3",
pages = "284--292",
month = mar,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Plovdiv, Plovdiv, Bulgaria",
bibno = "49659",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1988-10111",
journalabbrev = "J. Approx. Theory",
jrldate = "March 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Puoskari:1988:MCB,
author = "M. Puoskari",
title = "A method for computing {Bessel} function integrals",
journal = j-J-COMPUT-PHYS,
volume = "75",
number = "2",
pages = "334--344",
month = apr,
year = "1988",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(88)90116-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:40 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188901167",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Richardson:1988:NMT,
author = "Daniel Richardson",
title = "Nonstandard models of the theory of elementary
functions of a real variable",
journal = j-Z-MATH-LOGIK-GRUNDL-MATH,
volume = "34",
number = "4",
pages = "355--372",
year = "1988",
CODEN = "ZMLGAQ",
ISBN = "0044-3050",
ISBN-13 = "0044-3050",
ISSN = "0044-3050",
MRclass = "03B30 (03C62 03H15 26E35)",
MRnumber = "90a:03009",
MRreviewer = "Reuven H. Gurevi{\v{c}}",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ruscheweyh:1988:EST,
author = "Stephan Ruscheweyh",
title = "Extension of {Szeg{\H{o}}}'s theorem on the sections
of univalent functions",
journal = j-SIAM-J-MATH-ANA,
volume = "19",
number = "6",
pages = "1442--1449",
month = nov,
year = "1988",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58899",
catcode = "G.1.2; G.1.9; F.2.2; F.2.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.9 Integral Equations; G.1.9
Integro-differential equations; F.2.2 Nonnumerical
Algorithms and Problems; F.2.2 Computations on discrete
structures; F.2.2 Nonnumerical Algorithms and Problems;
F.2.2 Geometrical problems and computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
genterm = "algorithms; theory",
guideno = "1988-13739",
journalabbrev = "SIAM J. Math. Anal.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}
@InProceedings{Schwarz:1988:CLI,
author = "Jerry Schwarz",
title = "A {C++} Library for Infinite Precision Floating
Point",
crossref = "USENIX:1988:UPC",
pages = "271--281",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The Real library supports infinite precision floating
point computation in C++. Arbitrary precision rational
arithmetic and transcendental functions are
supported.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Laboratories, Murray Hill",
bookpages = "362",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "17--21 Oct. 1988",
conflocation = "Denver, CO, USA",
keywords = "C++ library; Infinite precision floating point;
Rational arithmetic; Real library; Transcendental
functions",
language = "English",
pubcountry = "USA",
thesaurus = "C language; Digital arithmetic; Object-oriented
programming; Subroutines",
}
@InProceedings{Sobczyk:1988:SMA,
author = "Kazimierz Sobczyk",
editor = "W. Schiehlen and W. Wedig",
booktitle = "Analysis and estimation of stochastic mechanical
systems",
title = "Stochastic modelling and analysis of fatigue",
volume = "303",
publisher = pub-SV,
address = pub-SV:adr,
pages = "269--313",
year = "1988",
ISBN = "0-387-82058-2",
ISBN-13 = "978-0-387-82058-3",
LCCN = "TA350.3.I5 no.303; TJ173 .A531 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Courses and lectures",
acknowledgement = ack-nhfb,
bibno = "58064",
bookpages = "350",
catcode = "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9",
CRclass = "J.2 Engineering; I.6.3 Applications; G.1.8 Partial
Differential Equations; G.1.8 Difference methods; G.3
Probabilistic algorithms (including Monte Carlo); G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.9 Integral Equations; G.1.9 Integro-differential
equations",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering; Computing Methodologies,
SIMULATION AND MODELING, Applications; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations, Difference methods; Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo); Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Integral Equations,
Integro-differential equations",
genterm = "algorithms; theory; design; measurement; reliability",
guideno = "1988-17476",
procdate = "1987",
procloc = "International Centre for Mechanical Sciences in
Udine",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; I. Computing Methodologies; I.6 SIMULATION
AND MODELING; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
waffil = "Univ. of Stuttgart; Univ. of Karlsruhe",
}
@Article{Stephens:1988:SCR,
author = "A. J. Stephens and H. C. Williams",
title = "Some computational results on a problem concerning
powerful numbers",
journal = j-MATH-COMPUT,
volume = "50",
number = "182",
pages = "619--632",
month = apr,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11R11 (11A51 11R27 11Y16 11Y40)",
MRnumber = "89d:11091",
MRreviewer = "H. J. Godwin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0210 (Algebra); B0250 (Combinatorial mathematics);
C1110 (Algebra); C1160 (Combinatorial mathematics)",
corpsource = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
Canada",
keywords = "computational complexity; continued; fractions; free
integer; fundamental unit; number theory; positive
square-; real quadratic number fields; regulator
algorithm Amdahl 5850; step algorithm; time complexity
$O(D^{1/4+\epsilon})$",
treatment = "T Theoretical or Mathematical; X Experimental",
}
@InProceedings{Stillinger:1988:CPS,
author = "Frank H. Stillinger",
editor = "Donald G. Truhlar",
booktitle = "Mathematical frontiers in computational chemical
physics",
title = "Collective phenomena in statistical mechanics and the
geometry of potential energy hypersurfaces",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "157--173",
year = "1988",
ISBN = "0-387-96782-6",
ISBN-13 = "978-0-387-96782-0",
LCCN = "QD455.3.M3 M38 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the Workshop on Atomic and Molecular
Structure and Dynamics, held June 15--July 24, 1987, at
the Institute for Mathematics and Its Applications,
University of Minnesota.",
price = "US\$36.80",
series = "The IMA volumes in mathematics and its applications",
acknowledgement = ack-nhfb,
bibno = "58051",
bookpages = "xii + 349",
catcode = "J.2; J.2; J.2; F.2.2; G.3; G.1.2",
CRclass = "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; G.3 Statistical computing;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Chemistry; Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Engineering; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations; Mathematics of Computing, PROBABILITY AND
STATISTICS, Statistical computing; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "algorithms; theory",
guideno = "1988-17776",
procdate = "1982",
procloc = "Univ. of Minnesota, Minneapolis",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING; J. Computer Applications; J.2
PHYSICAL SCIENCES AND ENGINEERING; F. Theory of
Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
waffil = "Univ. of Minnesota, Minneapolis",
}
@Article{Sun:1988:SAF,
author = "Xiehua Sun",
title = "On the simultaneous approximation of functions and
their derivatives by the {Szasz--Mirakyan} operator",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "279--288",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56048",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1988-10194",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@TechReport{Tang:1988:PIG,
author = "Ping Tak Peter Tang",
title = "Portable Implementation of a Generic Exponential
Function",
type = "Technical report",
number = "ANL-88-3",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1988",
bibdate = "Fri Dec 28 11:27:51 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{vanRijckevorsek:1988:CCA,
editor = "Jan L. A. van Rijckevorsek and Jan de Leeus",
title = "Component and correspondence analysis: dimension
reduction by functional approximation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 146",
year = "1988",
ISBN = "0-471-91847-4",
ISBN-13 = "978-0-471-91847-9",
LCCN = "QA278.5 .C6571 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$40",
series = "Wiley series in probability and mathematical
statistics",
acknowledgement = ack-nhfb,
bibno = "59092",
catcode = "G.1.2; G.3",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.3 Statistical computing",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing",
genterm = "theory; algorithms",
guideno = "1988-03042",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS",
}
@Book{Vilenkin:1988:SFT,
author = "N. Ja. (Naum Jakovlevich) Vilenkin",
title = "Special functions and the theory of group
representations",
volume = "22",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "x + 613",
year = "1988",
ISBN = "0-8218-1572-5",
ISBN-13 = "978-0-8218-1572-4",
LCCN = "QA3 .A5 v.22 1988",
bibdate = "Sat Oct 30 17:01:56 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Reprint of 1968 edition.",
series = "Translations of mathematical monographs",
acknowledgement = ack-nhfb,
subject = "Representations of groups; Functions, Special",
}
@Article{Wong:1988:AE,
author = "R. Wong",
title = "Asymptotic Expansion of $\int^{\pi/2}_0
{J}^2_\nu(\lambda \cos \theta) d\theta$",
journal = j-MATH-COMPUT,
volume = "50",
number = "181",
pages = "229--234",
month = jan,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "41A60 (33A40)",
MRnumber = "89g:41022",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); A0270
(Computational techniques); C4130 (Interpolation and
function approximation); C4160 (Numerical integration
and differentiation)",
corpsource = "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
Canada",
keywords = "asymptotic expansion; Bessel function; Bessel
functions; crystallography; diffraction theory;
function approximation; integral; integration",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Ahmed:1989:EEF,
author = "H. M. Ahmed",
title = "Efficient Elementary Function Generation with
Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "52--59",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
}
@Article{Armbruster:1989:KSD,
author = "Dieter Armbruster and John Guckenheimer and Philip
Holmes",
title = "{Kuramoto--Sivashinsky} dynamics on the
center-unstable manifold",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "676--691",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY;
Cornell Univ., Ithaca, NY",
bibno = "64938",
catcode = "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability; G.1.7 Ordinary Differential
Equations; G.1.7 Boundary value problems; G.1.0
General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.8 Partial Differential Equations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Physics; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09707",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Avellaneda:1989:OBE,
author = "Marco Avellaneda and Graeme W. Milton",
title = "Optimal bounds on the effective bulk modulus of
polycrystals",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "824--837",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64947",
catcode = "G.1.8; J.2; G.1.2; G.1.6",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Difference
methods; J.2 Physics; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.6 Optimization;
G.1.6 Constrained optimization",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Difference methods; Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Constrained optimization",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09716",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Belaga:1989:TMM,
author = "E. G. Belaga",
title = "Through the mincing machine with a {Boolean} layer
cake: nonstandard computations over {Boolean} circuits
in the lower-bounds-to-circuit-size complexity
proving",
journal = j-ACTA-INFO,
volume = "26",
number = "4",
pages = "381--407",
month = feb,
year = "1989",
CODEN = "AINFA2",
ISSN = "0001-5903 (print), 1432-0525 (electronic)",
ISSN-L = "0001-5903",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. Louis Pasteur, Strasbourg Cedex, France and
Univ. su Pisa, Pisa, Italy",
bibno = "69310",
catcode = "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2;
F.2.2",
CRclass = "F.4.1 Mathematical Logic; F.4.1 Computational logic;
B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1
Models of Computation; F.1.1 Unbounded-action devices;
F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Complexity of proof procedures;
F.1.2 Modes of Computation; F.1.2 Alternation and
nondeterminism; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Computations on discrete
structures",
descriptor = "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Computational logic;
Hardware, LOGIC DESIGN, Design Styles, Combinational
logic; Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Unbounded-action
devices; Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Complexity Classes; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Complexity of
proof procedures; Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Alternation and
nondeterminism; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures",
genterm = "algorithms; theory",
guideno = "1989-03239",
journalabbrev = "Acta Inf.",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND
FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; F. Theory of Computation; F.1 COMPUTATION BY
ABSTRACT DEVICES; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Birge:1989:SUB,
author = "John R. Birge and Roger J. Wets",
title = "Sublinear upper bounds for stochastic programs with
recourse",
journal = j-MATH-PROG,
volume = "43",
number = "2",
pages = "131--149",
month = feb,
year = "1989",
CODEN = "MHPGA4",
ISSN = "0025-5610",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Michigan, Ann Arbor; Univ. of California,
Davis",
bibno = "65226",
catcode = "G.1.6; G.1.7; G.3; G.1.6; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.7
Ordinary Differential Equations; G.1.7 Convergence and
stability; G.3 Probabilistic algorithms (including
Monte Carlo); G.1.6 Optimization; G.1.6 Gradient
methods; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Convergence and stability; Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo); Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization, Gradient
methods; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; theory; performance",
guideno = "1989-09042",
journalabbrev = "Math. Program.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Borwein:1989:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
title = "{Ramanujan}, modular equations, and approximations to
$\pi$ or how to compute one billion digits of $\pi$",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "3",
pages = "201--219",
month = mar,
year = "1989",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Dalhousie Univ., Halifax; Dalhousie Univ., Halifax",
bibno = "65243",
catcode = "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1",
CRclass = "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.8 Partial Differential Equations; G.1.8 Elliptic
equations; G.1.4 Quadrature and Numerical
Differentiation; G.1.4 Multiple quadrature; I.1.3
Languages and Systems; F.2.1 Numerical Algorithms and
Problems; F.2.1 Computation of transforms; F.2.1
Numerical Algorithms and Problems; F.2.1
Number-theoretic computations",
descriptor = "Computing Methodologies, ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations, Elliptic equations; Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Multiple quadrature; Computing
Methodologies, ALGEBRAIC MANIPULATION, Languages and
Systems; Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computation of transforms; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations",
genterm = "algorithms; theory",
guideno = "1989-03459",
journalabbrev = "Am. Math. Monthly",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Bos:1989:CPR,
author = "L. Bos",
title = "A characteristic of points in {$R^2$} having
{Lebesgue} function of polynomial growth",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "316--329",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72254",
catcode = "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on matrices; G.1.1 Interpolation; G.1.1
Interpolation formulas; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.2 Nonnumerical
Algorithms and Problems; F.2.2 Geometrical problems and
computations; G.1.2 Approximation; G.1.2 Chebyshev
approximation and theory; G.1.3 Numerical Linear
Algebra; G.1.3 Sparse and very large systems",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Mathematics of Computing,
NUMERICAL ANALYSIS, Interpolation, Interpolation
formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Chebyshev approximation and theory;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Sparse and very large systems",
genterm = "algorithms; theory",
guideno = "1989-07812",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Bronstein:1989:AIE,
author = "Manuel Bronstein",
title = "An algorithm for the integration of elementary
functions",
journal = j-LECT-NOTES-COMP-SCI,
volume = "378",
pages = "491--497",
year = "1989",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
MRclass = "65D30",
MRnumber = "91a:65050",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "EUROCAL '87 (Leipzig, 1987).",
acknowledgement = ack-nhfb,
}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
crossref = "ACM:1989:PAI",
pages = "207--211",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes an algorithm, based on Risch's
real structure theorem, that determines explicitly all
the algebraic relations among a given set of real
elementary functions. He provides examples from its
implementation in the Scratchpad computer algebra
system that illustrate the advantages over the use of
complex logarithms and exponentials.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Computer algebra system; Real elementary functions;
Real structure theorem; Scratchpad",
language = "English",
thesaurus = "Functions; Mathematics computing; Symbol
manipulation",
}
@Article{Cao:1989:ABS,
author = "J.-D. Cao and H. H. Gonska",
title = "Approximation by {Boolean} sums of positive linear
operators. {II}. {Gopengauz}-type estimates",
journal = j-J-APPROX-THEORY,
volume = "57",
number = "1",
pages = "77--89",
month = apr,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72266",
catcode = "G.1.2; G.1.2; G.3; G.2.1",
CRclass = "G.1.2 Approximation; G.1.2 Nonlinear approximation;
G.1.2 Approximation; G.1.2 Elementary function
approximation; G.3 Statistical computing; G.2.1
Combinatorics; G.2.1 Generating functions",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Nonlinear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions",
genterm = "algorithms; theory; measurement",
guideno = "1989-07823",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.2 DISCRETE
MATHEMATICS",
}
@Article{Carlson:1989:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals: Cubic Cases",
journal = j-MATH-COMPUT,
volume = "53",
number = "187",
pages = "327--333",
month = jul,
year = "1989",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65A05 (33A25 65D20)",
MRnumber = "89m:65009",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations); C1120 (Analysis)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
keywords = "cubic polynomial; elliptic; elliptic integral; first
kind; Fortran codes; functions; integral equations;
integrals; integration interval; R-; rational
integrands; real zeros; second kind; square root;
table; third kind",
treatment = "T Theoretical or Mathematical",
}
@Article{Chen:1989:EMB,
author = "X. R. Chen and P. R. Krishnaiah and W. W. Liang",
title = "Estimation of multivariate binary density using
orthogonal functions",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "178--186",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of
Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh,
Pittsburgh, PA",
bibno = "69313",
catcode = "D.3.3; G.3; G.1.3; G.1.2",
CRclass = "D.3.3 Language Constructs; D.3.3 Procedures,
functions, and subroutines; G.3 Statistical computing;
G.1.3 Numerical Linear Algebra; G.1.3 Linear systems
(direct and iterative methods); G.1.2 Approximation;
G.1.2 Elementary function approximation",
descriptor = "Software, PROGRAMMING LANGUAGES, Language Constructs,
Procedures, functions, and subroutines; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing; Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods); Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "algorithms; theory; verification",
guideno = "1989-08483",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
of Computing; G.3 PROBABILITY AND STATISTICS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Chen:1989:FCR,
author = "S.-G. Chen and P. Y. Hsieh",
title = "Fast computation of the ${N}$th root",
journal = j-COMP-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
month = "????",
year = "1989",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(89)90024-2",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Dec 29 08:01:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122189900242",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
remark = "From the abstract: ``A new class of iterative methods
for computing a differentiable function is proposed,
which is based on Pad{\'e} approximation to Taylor's
series of the function. It leads to a faster algorithm
than Newton's method for $x^{1/N}$ and a different
interpretation of Newton's method.''",
}
@Article{Corliss:1989:IIV,
author = "George Corliss and Gary Krenz",
editor = "L. Gatteschi",
title = "Indefinite Integration with Validation",
journal = j-TOMS,
volume = "15",
number = "4",
pages = "375--393",
month = dec,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D30 (65-04)",
MRnumber = "1 062 497",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/;
http://www.acm.org/pubs/toc/Abstracts/toms/76915.html",
acknowledgement = ack-nhfb,
bibno = "393",
content = "ALGORITHMS; THEORY",
CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.2 Approximation; G.1.2 Chebyshev approximation and
theory",
CRnumber = "1989-03199",
descriptor = "mathematics of computing, numerical analysis,
quadrature and numerical differentiation; mathematics
of computing, numerical analysis, approximation,
elementary function approximation; mathematics of
computing, numerical analysis, approximation, Chebyshev
approximation and theory",
fortitle = "ACM Trans. Math. Softw.",
guideno = "4",
keywords = "algorithms; theory",
review = "ACM CR 9007-0598",
subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.1.2}: Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory.",
waffil = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Critchfield:1989:CEF,
author = "Charles L. Critchfield",
title = "Computation of elliptic functions",
journal = j-J-MATH-PHYS,
volume = "30",
number = "2",
pages = "295--297",
month = feb,
year = "1989",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.528444",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A25 (65D20)",
MRnumber = "89k:33004",
MRreviewer = "H. Hochstadt",
bibdate = "Mon Oct 31 11:58:32 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v30/i2/p295_s1",
acknowledgement = ack-nhfb,
pagecount = "3",
}
@Misc{Darley:1989:FPI,
author = "H. M. Darley and others",
title = "Floating Point\slash Integer Processor with Divide and
Square Root Functions",
year = "1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 4,878,190.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Dehling:1989:FLI,
author = "Herold Dehling",
title = "The functional law of the iterated logarithm for {von
Mises} functionals and multiple {Wiener} integrals",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "177--189",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG",
bibno = "64336",
catcode = "G.3; G.1.9; G.1.2",
CRclass = "G.3 Statistical computing; G.1.9 Integral Equations;
G.1.9 Integro-differential equations; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Integral Equations,
Integro-differential equations; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "algorithms; theory; measurement",
guideno = "1989-08462",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Demirbas:1989:MSE,
author = "K. Demirbas",
title = "Multidimensional state estimation using stacks for
dynamic systems with interference",
journal = j-AUTOMATICA,
volume = "25",
number = "4",
pages = "617--621",
month = jul,
year = "1989",
CODEN = "ATCAA9",
ISSN = "0005-1098",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72661",
catcode = "G.1.2; G.1.2; G.1.3; G.1.5; H.1.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Linear
approximation; G.1.3 Numerical Linear Algebra; G.1.3
Linear systems (direct and iterative methods); G.1.5
Roots of Nonlinear Equations; H.1.1 Systems and
Information Theory; H.1.1 Information theory",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods);
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Information Systems, MODELS AND
PRINCIPLES, Systems and Information Theory, Information
theory",
genterm = "algorithms; theory",
guideno = "1989-03952",
jrldate = "July 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H.
Information Systems; H.1 MODELS AND PRINCIPLES",
}
@TechReport{Dritz:1989:RPS,
author = "K. W. Dritz",
title = "Rationale for the Proposed Standard for a Generic
Package of Elementary Functions for {Ada}",
type = "Report",
number = "ANL-89/2 Rev. 1",
institution = "Argonne National Laboratory, Mathematics and Computer
Science Division",
address = "Argonne, IL, USA",
pages = "????",
month = oct,
year = "1989",
bibdate = "Thu Sep 01 12:08:24 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@InProceedings{Duprat:1989:SRA,
author = "J. Duprat and Y. Herreros and J.-M. Muller",
title = "Some results about on-line computation of functions",
crossref = "Ercegovac:1989:PSC",
pages = "112--118",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dyn:1989:PEB,
author = "N. Dyn and A. Ron",
title = "Periodic exponential box splines on a three direction
mesh",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "287--296",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72251",
catcode = "G.1.2; F.2.2; G.1.2; G.1.2; G.1.2; G.2.1; G.3",
CRclass = "G.1.2 Approximation; G.1.2 Spline and piecewise
polynomial approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations; G.1.2 Approximation; G.1.2 Chebyshev
approximation and theory; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.2 Approximation;
G.1.2 Linear approximation; G.2.1 Combinatorics; G.2.1
Recurrences and difference equations; G.3 Statistical
computing",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Chebyshev approximation and
theory; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, DISCRETE MATHEMATICS, Combinatorics,
Recurrences and difference equations; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing",
genterm = "algorithms; theory; design",
guideno = "1989-07809",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3
PROBABILITY AND STATISTICS",
}
@Article{Eberlein:1989:SAC,
author = "E. Eberlein",
title = "Strong approximation of continuous time stochastic
processes",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "220--235",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. Freiburg, Freiburg, W. Germany",
bibno = "69316",
catcode = "D.4.8; F.1.2; G.1.2",
CRclass = "D.4.8 Performance; D.4.8 Stochastic analysis; F.1.2
Modes of Computation; F.1.2 Probabilistic computation;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Software, OPERATING SYSTEMS, Performance, Stochastic
analysis; Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Probabilistic
computation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; performance; theory",
guideno = "1989-08486",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "D. Software; D.4 OPERATING SYSTEMS; F. Theory of
Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Egger:1989:PAC,
author = "A. Egger and R. Huotari",
title = "The {Polya} algorithm on convex sets",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "2",
pages = "212--216",
month = feb,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72242",
catcode = "F.2.2; F.2.2; G.1.2; G.1.2; G.1.5",
CRclass = "F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Geometrical problems and computations; F.2.2
Nonnumerical Algorithms and Problems; F.2.2
Computations on discrete structures; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.2 Approximation; G.1.2 Minimax approximation and
algorithms; G.1.5 Roots of Nonlinear Equations; G.1.5
Convergence",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations; Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Convergence",
genterm = "algorithms; theory",
guideno = "1989-07801",
journalabbrev = "J. Approx. Theory",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Ehrenmark:1989:ONF,
author = "Ulf T. Ehrenmark",
title = "Overconvergence of the near-field expansion for
linearized waves normally incident on a sloping beach",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "799--815",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64945",
catcode = "G.1.7; G.1.2; F.2.1; G.1.2; F.2.2",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability; G.1.2 Approximation; G.1.2
Minimax approximation and algorithms; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Minimax approximation and algorithms;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09714",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Einmahl:1989:ERK,
author = "U. Einmahl",
title = "Extensions of results of {Komlos}, {Major}, and
{Tusnady} to the multivariate case",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "1",
pages = "20--68",
month = jan,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. zu Koln, West Germany",
bibno = "66700",
catcode = "G.3; G.1.2; F.2.1",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computation of transforms",
genterm = "algorithms; theory",
guideno = "1989-08456",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Jan. 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Epperson:1989:UIM,
author = "J. F. Epperson",
title = "On the use of iteration methods for approximating the
natural logarithm",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "9",
pages = "831--835",
month = nov,
year = "1989",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26A06 (26A09)",
MRnumber = "91a:26002",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "71703",
catcode = "G.1.2; G.1.2; K.3.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation; K.3.2 Computer and
Information Science Education",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Computing Milieux, COMPUTERS AND
EDUCATION, Computer and Information Science Education",
genterm = "algorithms; theory",
guideno = "1989-03518",
journalabbrev = "Am. Math. Monthly",
jrldate = "Nov. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K.
Computing Milieux; K.3 COMPUTERS AND EDUCATION",
}
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding for division and square root",
crossref = "Ercegovac:1989:PSC",
pages = "169--173",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "In division and square root implementation based on
digit-recurrence algorithms, the result is obtained in
digit-serial form, from most significant digit to least
significant. To reduce the complexity of the
result-digit selection and to allow the \ldots{}",
}
@InProceedings{Ercegovac:1989:IMC,
author = "M. D. Ercegovac and T. Lang",
booktitle = "IEEE International Symposium on Circuits and Systems,
8--11 May 1989",
title = "Implementation of module combining multiplication,
division, and square root",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "150--153",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The implementation of a module that performs radix-$2$
multiplication, division, and square root is presented.
The module is compact because most of the components
are shared by all three operations, the complexity
being similar to that of a radix-$2$ \ldots{}",
}
@InProceedings{Ercegovac:1989:RSR,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Radix-4 square root without initial {PLA}",
crossref = "Ercegovac:1989:PSC",
pages = "162--168",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "A systematic derivation of a radix-$4$ square root
algorithm using redundance in the partial residuals and
the result is presented. Unlike other similar schemes,
the algorithm does not use a table-lookup or
programmable logic array (PLA) for the \ldots{}",
}
@InProceedings{Fandrianto:1989:AHS,
author = "Jan Fandrianto",
title = "Algorithms for high-speed shared radix 8 division and
radix 8 square root",
crossref = "Ercegovac:1989:PSC",
pages = "68--75",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-9",
summary = "An algorithm for performing radix-$8$ division and
square root in a shared hardware is described. To
achieve short iteration cycle time, it utilizes an
optimized `next quotient/root prediction PLA' generally
used in a radix-$4$ SRT division with minimal
\ldots{}",
}
@Article{Ge:1989:OCL,
author = "Renpu Ge",
title = "Optimal choice of linear interval extension",
journal = j-APPL-MATH-COMP,
volume = "30",
number = "2",
pages = "165--189",
month = mar,
year = "1989",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64710",
catcode = "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1;
G.1.0",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Linear approximation; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.1 Combinatorics; G.2.1 Combinatorial algorithms;
F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Computations on discrete structures; G.1.2
Approximation; G.1.2 Minimax approximation and
algorithms; G.1.1 Interpolation; G.1.1 Difference
formulas; G.1.0 General; G.1.0 Numerical algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Linear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Combinatorial algorithms;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Minimax approximation and algorithms;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Difference formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms",
genterm = "algorithms; theory; measurement",
guideno = "1989-03670",
journalabbrev = "Appl. Math. Comput.",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS",
}
@Article{Gersch:1989:SPT,
author = "W. Gersch and G. Kitagawa",
title = "Smoothness priors transfer function estimation",
journal = j-AUTOMATICA,
volume = "25",
number = "4",
pages = "603--608",
month = jul,
year = "1989",
CODEN = "ATCAA9",
ISSN = "0005-1098",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72658",
catcode = "G.1.1; G.1.2; G.1.6",
CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.6 Optimization; G.1.6 Gradient methods",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Smoothing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization, Gradient methods",
genterm = "algorithms; theory",
guideno = "1989-03949",
jrldate = "July 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InCollection{Glover:1989:THN,
author = "Keith Glover",
editor = "Jan C. Willems",
booktitle = "From data to model",
title = "A tutorial on {Hankel}-norm approximation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "26--48",
year = "1989",
ISBN = "0-387-51571-2",
ISBN-13 = "978-0-387-51571-7",
LCCN = "QA279 .F76 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "70545",
bookpages = "246",
catcode = "G.1.2; F.2.1; F.2.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; F.2.1 Numerical Algorithms and Problems;
F.2.1 Computations on matrices; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computation of
transforms",
genterm = "algorithms; theory",
guideno = "1989-01692",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
waffil = "Univ. of Groningen, Groningen, The Netherlands",
}
@InProceedings{Glynn:1989:OSS,
author = "P. W. Glynn",
editor = "Edward A. MacNair and Kenneth J. Musselman and Philip
Heidelberger",
booktitle = "1989 Winter Simulation Conference proceedings:
December 4--6, 1989, the Capital Hilton Hotel,
Washington, DC",
title = "Optimization of stochastic systems via simulation",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "90--105",
year = "1989",
ISBN = "0-911801-58-8",
ISBN-13 = "978-0-911801-58-3",
LCCN = "QA76.9.C65 W56 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE order no. 89CH2778-9.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
acknowledgement = ack-nhfb,
bibno = "76750",
bookpages = "xx + 1139",
catcode = "I.6.3; G.1.6; G.3; G.1.2",
CRclass = "I.6.3 Applications; G.1.6 Optimization; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Applications; Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization; Mathematics of Computing,
PROBABILITY AND STATISTICS; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; design; performance",
guideno = "1989-12012",
procdate = "December 4-6, 1989",
procloc = "Washington, D. C.",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
AND STATISTICS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Gomes:1989:GGL,
author = "M. I. Gomes",
title = "Generalized {Gumbel} and likelihood ratio test
statistics in the multivariate {GEV} model",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "7",
number = "3",
pages = "259--267",
month = feb,
year = "1989",
CODEN = "CSDADW",
ISSN = "0167-9473",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "70043",
catcode = "G.3; G.1.7; I.5.1; G.1.6; G.1.2",
CRclass = "G.3 Statistical computing; G.1.7 Ordinary Differential
Equations; G.1.7 Convergence and stability; I.5.1
Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6
Nonlinear programming; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations,
Convergence and stability; Computing Methodologies,
PATTERN RECOGNITION, Models, Statistical; Mathematics
of Computing, NUMERICAL ANALYSIS, Optimization,
Nonlinear programming; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; measurement; reliability; theory",
guideno = "1989-04403",
journalabbrev = "Comput. Stat. Data Anal.",
jrldate = "Feb. 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; I. Computing Methodologies; I.5 PATTERN
RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@InProceedings{Gonzaga:1989:ASL,
author = "Cl{\'o}vis C. Gonzaga",
title = "An algorithm for solving linear programming programs
in {$O(n^3L)$} operations",
crossref = "Megiddo:1989:PMP",
pages = "1--28",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74172",
catcode = "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Elementary function approximation;
F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on matrices; I.1.2 Algorithms; I.1.2
Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis
of algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms; Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms",
genterm = "algorithms; theory",
guideno = "1989-12474",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@TechReport{Gragg:1989:FSE,
author = "W. Gragg and B. Neta",
title = "Fortran Subroutines for the Evaluation of the
Confluent Hypergeometric Functions",
number = "NPS-MA-89-014",
institution = inst-MATH-NPS,
address = inst-MATH-NPS:adr,
year = "1989",
bibdate = "Fri Nov 11 14:50:24 MST 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/n/neta-beny.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Software available URL http://math.nps.navy.mil",
}
@Article{Guo:1989:RCS,
author = "S.-S. Guo and M. K. Khan",
title = "On the rate of convergence of some operators on
functions of bounded variation",
journal = j-J-APPROX-THEORY,
volume = "58",
number = "1",
pages = "90--101",
month = jul,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "69424",
catcode = "F.2.1; G.1.2",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on polynomials; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; theory",
guideno = "1989-07854",
journalabbrev = "J. Approx. Theory",
jrldate = "July 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Hornik:1989:MFN,
author = "K. Hornik and M. Stinchcombe and H. White",
title = "Multilayer feedforward networks are universal
approximators",
journal = j-NEURAL-NETWORKS,
volume = "2",
number = "5",
pages = "359--366",
year = "1989",
CODEN = "NNETEB",
ISSN = "0893-6080",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Technisce Univ. Wien, Vienna, Austria; Univ. of
California, San Diego; Univ. of California, San Diego",
bibno = "70408",
catcode = "F.2.1; G.1.2; F.1.1; I.2.4",
CRclass = "F.2.1 Numerical Algorithms and Problems; G.1.2
Approximation; G.1.2 Elementary function approximation;
F.1.1 Models of Computation; F.1.1 Unbounded-action
devices; I.2.4 Knowledge Representation Formalisms and
Methods",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Models of Computation, Unbounded-action devices;
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Knowledge Representation Formalisms and Methods",
genterm = "design; performance",
guideno = "1989-09273",
journalabbrev = "Neural Networks",
jrldate = "1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1
COMPUTATION BY ABSTRACT DEVICES; I. Computing
Methodologies; I.2 ARTIFICIAL INTELLIGENCE",
}
@Article{Jamieson:1989:RCI,
author = "M. J. Jamieson",
title = "Rapidly converging iterative formulae for finding
square roots and their computational efficiencies",
journal = j-COMP-J,
volume = "32",
number = "1",
pages = "93--94",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/32.1.93",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65H05",
MRnumber = "89k:65063",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/",
note = "This work generalizes the Pythagorean sums in
\cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
abstract = "A derivation is given of rapidly converging iterative
formulae for finding square roots which include, as
special cases, some recently published examples. Their
computational efficiencies are investigated for
sequential and parallel implementation. It is concluded
that the most efficient method is equivalent to
sequential application of the Newton Raphson formula; a
simple modification is suggested which brings the
advantage of root bracketing at little extra
computational cost.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Glasgow Univ., UK",
affiliationaddress = "Glasgow, Scotl",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921; B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Dept. of Comput. Sci., Glasgow Univ., UK",
keywords = "computational; Computational efficiencies;
Computational Efficiency; Computer Metatheory;
Convergence; convergence of numerical methods;
Converging iterative formulae; converging iterative
formulae; efficiencies; formula; function
approximation; Iterative Methods; iterative methods;
Newton Raphson; Newton Raphson formula, Mathematical
Techniques; Parallel implementation; parallel
implementation; Square Roots; Square roots; square
roots",
thesaurus = "Convergence of numerical methods; Function
approximation; Iterative methods",
treatment = "P Practical",
}
@Article{Jeffries:1989:GFA,
author = "John S. Jeffries and Donald R. Smith",
title = "A {Green} function approach for a singularly perturbed
vector boundary-value problem",
journal = j-ADV-APPL-MATH,
volume = "10",
number = "1",
pages = "1--50",
month = mar,
year = "1989",
CODEN = "????",
ISSN = "0196-8858",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California at San Diego, La Jolla; Univ. of
California at San Diego, La Jolla",
bibno = "64833",
catcode = "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Boundary
value problems; G.1.7 Ordinary Differential Equations;
G.1.7 Convergence and stability; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms; G.1.2 Approximation; G.1.2 Nonlinear
approximation; G.1.3 Numerical Linear Algebra; G.1.3
Eigenvalues; G.1.2 Approximation; G.1.2 Elementary
function approximation; G.1.3 Numerical Linear Algebra;
G.1.3 Linear systems (direct and iterative methods)",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Nonlinear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods)",
genterm = "algorithms; theory",
guideno = "1989-03271",
journalabbrev = "Adv. Appl. Math.",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Johnson:1989:IMA,
author = "K. R. Johnson",
title = "An Iterative Method for Approximating Square Roots",
journal = j-MATH-MAG,
volume = "62",
number = "4",
pages = "253--259",
month = oct,
year = "1989",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kaishev:1989:SSC,
author = "A. I. Kaishev",
title = "A sharpened scheme for constructing an a posteriori
interval extension of an elementary function.
({Russian})",
journal = "Voprosy Kibernet. (Moscow)",
volume = "149",
pages = "14--18",
year = "1989",
ISBN = "0134-6388",
ISBN-13 = "0134-6388",
MRclass = "65G10",
MRnumber = "91i:65090",
MRreviewer = "I. N. Molchanov",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kak:1989:BAS,
author = "S. C. Kak and A. O. Barbir",
booktitle = "Proceedings of the Twenty-First Southeastern Symposium
on System Theory, 26--28 March 1989",
title = "The {Brahmagupta} algorithm for square rooting",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "456--459",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root evaluation is introduced.
Novel features of the algorithm include suitability for
parallel processing and multi-initial guesses of the
root. An extension of the algorithm to the nth rooting
is provided. A VLSI \ldots{}",
}
@Article{Kogan:1989:GBF,
author = "B. J. Kogan",
title = "General background of functional memory algorithms",
journal = j-TRANS-SOC-COMP-SIM,
volume = "5",
number = "4",
pages = "285--317",
month = oct,
year = "1989",
CODEN = "TSCSEV",
ISSN = "0740-6797",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California, Los Angeles",
bibno = "69149",
catcode = "C.3; G.1.2; G.1.2; E.4",
CRclass = "C.3 Signal processing systems; G.1.2 Approximation;
G.1.2 Elementary function approximation; G.1.2
Approximation; G.1.2 Linear approximation; E.4 Data
compaction and compression",
descriptor = "Computer Systems Organization, SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS, Signal processing systems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Data, CODING AND
INFORMATION THEORY, Data compaction and compression",
genterm = "algorithms; design",
guideno = "1989-10680",
journalabbrev = "Trans. Soc. Comput. Simul.",
jrldate = "Oct. 1989",
subject = "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
AND APPLICATION-BASED SYSTEMS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING
AND INFORMATION THEORY",
}
@InProceedings{Kojima:1989:PDI,
author = "M. Kojima and S. Mizuno and A. Yoshise",
title = "A primal-dual interior point algorithm for linear
programming",
crossref = "Megiddo:1989:PMP",
pages = "29--47",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74173",
bookpages = "x + 158",
catcode = "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.1
Numerical Algorithms and Problems; G.1.2 Approximation;
G.1.2 Elementary function approximation; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; F.2.1 Numerical Algorithms
and Problems; F.2.1 Computations on matrices; I.1.2
Algorithms; I.1.2 Algebraic algorithms; I.1.2
Algorithms; I.1.2 Analysis of algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations; Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms; Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms",
genterm = "algorithms; theory",
guideno = "1989-12475",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Kraaikamp:1989:SEP,
author = "Cor Kraaikamp",
title = "Statistic and ergodic properties of {Minkowski}'s
diagonal continued fraction",
journal = j-THEOR-COMP-SCI,
volume = "65",
number = "2",
pages = "197--212",
day = "28",
month = jun,
year = "1989",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Amsterdam Univ., Amsterdam, The Netherlands and Univ.
de Provence, Marseille, France",
bibno = "70095",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; theory",
guideno = "1989-10594",
journalabbrev = "Theor. Comput. Sci.",
jrldate = "28 June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Kreider:1989:WSA,
author = "K. L. Kreider",
title = "A wave splitting approach to time dependent inverse
scattering for the stratified cylinder",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "932--943",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64953",
catcode = "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Initial
value problems; G.1.2 Approximation; G.1.2 Elementary
function approximation; J.2 Physics; J.2 Electronics;
F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Geometrical problems and computations; G.1.3 Numerical
Linear Algebra; G.1.3 Linear systems (direct and
iterative methods); I.1.1 Expressions and Their
Representation; I.1.1 Simplification of expressions",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Initial value problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Electronics; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations; Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods);
Computing Methodologies, ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions",
genterm = "algorithms; theory; experimentation; measurement",
guideno = "1989-09722",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I.
Computing Methodologies; I.1 ALGEBRAIC MANIPULATION",
}
@PhdThesis{Littlestone:1989:MBL,
author = "N. Littlestone",
title = "Mistake bounds and logarithmic linear-threshold
learning algorithms",
type = "{Ph.D} Thesis",
school = "University of California at Santa Cruz",
address = "Santa Cruz, CA, USA",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76493",
catcode = "I.2.6; J.4; H.1.2; G.1.2",
CRclass = "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine
Systems; H.1.2 Human information processing; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Learning; Computer Applications, SOCIAL AND BEHAVIORAL
SCIENCES, Psychology; Information Systems, MODELS AND
PRINCIPLES, User/Machine Systems, Human information
processing; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; human factors; performance",
guideno = "1989-12934",
source = "UMI Order No: GAX89-26506",
subject = "I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND
BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS
AND PRINCIPLES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Lo:1989:RBP,
author = "Shaw-Hwa Lo and Jane-Ling Wang",
title = "Representations for the bivariate product limit
estimators and the bootstrap versions",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "211--226",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California, Davis; Univ. of California,
Davis",
bibno = "64339",
catcode = "G.3; G.1.2; G.1.4; G.1.7",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.4 Quadrature and
Numerical Differentiation; G.1.4 Gaussian quadrature;
G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation,
Gaussian quadrature; Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations,
Convergence and stability",
genterm = "algorithms; theory; measurement",
guideno = "1989-08465",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.3 PROBABILITY AND STATISTICS",
}
@Article{Lorentz:1989:NA,
author = "G. G. Lorentz",
title = "Notes on approximation",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "360--365",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72258",
catcode = "G.1.1; G.1.2; G.1.1",
CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.1 Interpolation; G.1.1 Spline and piecewise
polynomial interpolation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Smoothing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Spline and piecewise
polynomial interpolation",
genterm = "algorithms; theory",
guideno = "1989-07816",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Lu:1989:VMI,
author = "P. Y. Lu and K. Dawallu",
title = "A {VLSI} Module for {IEEE} Floating-Point
Multiplication\slash Division\slash Square Root",
crossref = "IEEE:1989:PII",
pages = "366--368",
year = "1989",
bibdate = "Wed Nov 06 12:08:38 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The major objective of this VLSI module design is to
determine how to modify a fast floating-point
multiplier so that it can perform division and square
root in accordance with IEEE standards. This has been
achieved by applying the Newton-Ralphson iteration only
on the mantissa and adjusting the iterated result by a
rounding algorithm. Using 1.0- mu m CMOS standard cell
technology, the total area of this module is
approximately 7.0 mm*6.5 mm, which is just 25\% larger
than the floating-point multiplier. The module can
compute multiplication, division, and square root in 3,
31, and 43 cycles, respectively. The cycle time, under
nominal conditions, is expected to be 20 ns. (2
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "LSI Logic Corp., Menlo Park, CA, USA",
bookpages = "xvii + 587",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
keywords = "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
technology; Cycle time; Fast floating-point multiplier;
Floating point division; Floating point square root;
IEEE standards; Iterated result; Mantissa; Multiplier
modification; Newton-Ralphson iteration; Rounding
algorithm; VLSI module design",
numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
7.0E-03 m",
thesaurus = "Cellular arrays; CMOS integrated circuits; Digital
arithmetic; Dividing circuits; Iterative methods;
Modules; Multiplying circuits; VLSI",
}
@Article{Macleod:1989:SAA,
author = "Allan J. Macleod",
title = "Statistical Algorithms: {Algorithm AS 245}: {A} Robust
and Reliable Algorithm for the Logarithm of the Gamma
Function",
journal = j-APPL-STAT,
volume = "38",
number = "2",
pages = "397--402",
month = jun,
year = "1989",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
bibdate = "Sat Apr 21 10:25:27 MDT 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/245",
acknowledgement = ack-nhfb,
}
@InProceedings{Mansour:1989:CAS,
author = "Y. Mansour and B. Schieber and P. Tiwari",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "The complexity of approximating the square root",
crossref = "IEEE:1989:ASF",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "325--330",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors prove upper and lower bounds for
approximately computing the square root using a given
set of operations. The bounds are extended to hold for
approximating the kth root, for any fixed k. Several
tools from approximation \ldots{}",
}
@Article{Martin:1989:TPQ,
author = "Pablo Martin and Antonio Luis Guerrero",
title = "Two-point quasi-fractional approximations to the
{Bessel} function {$J_\nu(x)$} of fractional order",
journal = j-J-COMPUT-PHYS,
volume = "85",
number = "2",
pages = "487--492",
month = dec,
year = "1989",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(89)90161-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:48 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999189901617",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
remark = "This work produces only 3D approximations.",
}
@InProceedings{Megiddo:1989:POS,
author = "N. Megiddo",
title = "Pathways to the optimal set in linear programming",
crossref = "Megiddo:1989:PMP",
pages = "131--158",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74179",
catcode = "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4;
G.4",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.2 Graph Theory; G.2.2 Path and circuit problems;
G.1.2 Approximation; G.1.2 Spline and piecewise
polynomial approximation; G.1.5 Roots of Nonlinear
Equations; G.1.5 Iterative methods; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations on
matrices; I.1.2 Algorithms; I.1.2 Analysis of
algorithms; G.4 Algorithm analysis; G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, DISCRETE MATHEMATICS, Graph Theory, Path and
circuit problems; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Spline and piecewise
polynomial approximation; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Iterative methods; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices; Computing
Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
Analysis of algorithms; Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics
of Computing, MATHEMATICAL SOFTWARE, Efficiency",
genterm = "algorithms; performance; theory",
guideno = "1989-12481",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing;
G.4 MATHEMATICAL SOFTWARE",
}
@PhdThesis{Miler:1989:EEM,
author = "T. H. Miler",
title = "Error evaluation of microcomputer intrinsic
functions",
type = "{Ph.D} Thesis",
school = "University of Idaho",
address = "Moscow, ID",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76168",
catcode = "G.4; G.1.2; J.2",
CRclass = "G.4 Reliability and robustness; G.1.2 Approximation;
G.1.2 Elementary function approximation; J.2
Mathematics and statistics",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Computer Applications, PHYSICAL SCIENCES
AND ENGINEERING, Mathematics and statistics",
genterm = "algorithms; reliability",
guideno = "1989-12941",
source = "UMI order no: GAX89-22813",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING",
}
@InProceedings{Montuschi:1989:EIH,
author = "Paolo Montuschi and Luigi Cinimera",
title = "On the efficient implementation of higher radix square
root algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "154--161",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "Square root nonrestoring algorithms operating with a
radix higher than two (but power of 2) are discussed.
Formulas are derived delimiting the feasibility space
of the class of algorithms considered as a function of
the different parameters. This \ldots{}",
}
@Book{Moshier:1989:MPM,
author = "Stephen L. B. Moshier",
title = "Methods and Programs for Mathematical Functions",
publisher = pub-ELLIS-HORWOOD,
address = pub-ELLIS-HORWOOD:adr,
pages = "vii + 415",
year = "1989",
ISBN = "0-7458-0289-3",
ISBN-13 = "978-0-7458-0289-3",
LCCN = "QA331 .M84 1989",
bibdate = "Thu Sep 01 10:33:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\pounds 48.00",
acknowledgement = ack-nj,
}
@Article{Rhee:1989:MII,
author = "W. T. Rhee and M. Talagrand",
title = "Martingale inequalities, interpolation and
{NP}-complete problems",
journal = j-MATH-OP-RES,
volume = "14",
number = "1",
pages = "91--96",
month = feb,
year = "1989",
CODEN = "MOREDQ",
ISSN = "0364-765X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ., Paris, Paris, France; Ohio State Univ.,
Columbus",
bibno = "67063",
catcode = "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3",
CRclass = "G.2.2 Graph Theory; G.2.2 Path and circuit problems;
H.1.1 Systems and Information Theory; H.1.1 General
systems theory; G.1.1 Interpolation; G.1.1
Interpolation formulas; G.1.2 Approximation; G.1.2
Elementary function approximation; G.3 Probabilistic
algorithms (including Monte Carlo); I.6.4 Model
Validation and Analysis; F.1.3 Complexity Classes;
F.1.3 Reducibility and completeness",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Path and circuit problems; Information Systems,
MODELS AND PRINCIPLES, Systems and Information Theory,
General systems theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Interpolation, Interpolation
formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, PROBABILITY AND STATISTICS,
Probabilistic algorithms (including Monte Carlo);
Computing Methodologies, SIMULATION AND MODELING, Model
Validation and Analysis; Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Classes,
Reducibility and completeness",
genterm = "algorithms; theory; measurement",
guideno = "1989-09079",
journalabbrev = "Math. Oper. Res.",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND
STATISTICS; H. Information Systems; H.1 MODELS AND
PRINCIPLES; I. Computing Methodologies; I.6 SIMULATION
AND MODELING",
}
@Article{Ruymgaart:1989:SPB,
author = "F. H. Ruymgaart",
title = "Some properties of bivariate empirical hazard
processes under random censoring",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "271--281",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64343",
catcode = "G.3; G.1.2",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; theory; measurement",
guideno = "1989-08469",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@InCollection{Saigo:1989:FID,
author = "Megumi Saigo",
title = "Fractional integrals and derivatives associated with
elementary functions and {Bessel} functions",
crossref = "Srivastava:1989:UFF",
pages = "283--306",
year = "1989",
MRclass = "26A33 (33C10)",
MRnumber = "93h:26011",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Ellis Horwood Ser. Math. Appl.",
acknowledgement = ack-nhfb,
}
@Article{Sala:1989:TJA,
author = "Kenneth L. Sala",
title = "Transformations of the {Jacobian} amplitude function
and its calculation via the arithmetic-geometric mean",
journal = j-SIAM-J-MATH-ANA,
volume = "20",
number = "6",
pages = "1514--1528",
month = nov,
year = "1989",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A25 (42A16 70D99)",
MRnumber = "90j:33003",
MRreviewer = "J. M. H. Peters",
bibdate = "Sun Nov 28 19:24:55 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Smith:1989:EMP,
author = "David M. Smith",
title = "Efficient multiple-precision evaluation of elementary
functions",
journal = j-MATH-COMPUT,
volume = "52",
number = "185",
pages = "131--134",
month = jan,
year = "1989",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D15 (26-04)",
MRnumber = "90c:65034",
MRreviewer = "Menachem Dishon",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Dept. of Math., Loyola Univ., Los Angeles, CA, USA",
keywords = "arithmetic; base b; elementary functions; function
evaluation; multiple-precision evaluation",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Stearns:1989:SFD,
author = "C. C. Stearns",
title = "Subtractive floating-point division and square root
for {VLSI DSP}",
crossref = "IEE:1989:EEC",
pages = "405--409",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard deviation computations,
and general purpose processing are discussed. Emphasis
here is on the internal architectures of the arithmetic
units not on their applications. The research presented
in this paper has been proven feasible and reliable
from extensive gate-level simulation and fabrication in
silicon.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570D (CMOS integrated circuits);
C5230 (Digital arithmetic methods); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Adaptive filtering; Arithmetic units; CMOS technology;
Floating point division; Floating point square root
architectures; Gate-level simulation; General purpose
processing; Real-time digital signal processing;
Semiconductor; Standard deviation computations; VLSI
DSP",
thesaurus = "Adaptive filters; CMOS integrated circuits; Digital
arithmetic; Digital signal processing chips; VLSI",
}
@TechReport{Tang:1989:TCA,
author = "Ping Tak Peter Tang",
title = "Testing Computer Arithmetic by Elementary Number
Theory",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
address = "Argonne, IL, USA",
pages = "????",
month = aug,
year = "1989",
bibdate = "Fri Jun 11 12:38:06 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Tang:1989:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Exponential
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "144--157",
month = jun,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Sep 04 22:47:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/63522.214389;
http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
abstract = "Algorithms and implementation details for the
exponential function in both single- and
double-precision of IEEE 754 arithmetic are presented
here. With a table of moderate size, the
implementations need only working-precision arithmetic
and are provably accurate to within 0.54 ulp as long as
the final result does not underflow. When the final
result suffers gradual underflow, the error is still no
worse than 0.77 ulp.",
acknowledgement = ack-nj,
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Article{Ubhaya:1989:LAN,
author = "V. A. Ubhaya",
title = "{$L_p$} approximation from nonconvex subsets of
special classes of functions",
journal = j-J-APPROX-THEORY,
volume = "57",
number = "2",
pages = "223--238",
month = may,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72277",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1989-07833",
journalabbrev = "J. Approx. Theory",
jrldate = "May 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Vaidya:1989:LWB,
author = "P. M. Vaidya",
title = "A locally well-behaved potential function and a simple
{Newton}-type method for finding the center of a
polytype",
crossref = "Megiddo:1989:PMP",
pages = "79--90",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74176",
catcode = "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.6
Optimization; G.1.6 Gradient methods; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.5 Roots of
Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of
Nonlinear Equations; G.1.5 Iterative methods; I.1.2
Algorithms; I.1.2 Nonalgebraic algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization, Gradient
methods; Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Convergence; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Iterative methods; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms",
genterm = "algorithms; theory",
guideno = "1989-12478",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
xxpages = "131--158",
}
@PhdThesis{Vavasis:1989:CFP,
author = "S. A. Vavasis",
title = "Complexity of fixed point computations",
type = "{Ph.D} Thesis",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76220",
catcode = "J.4; G.1.2; F.1.3; G.1.2; G.2.2",
CRclass = "J.4 Economics; G.1.2 Approximation; G.1.2 Nonlinear
approximation; F.1.3 Complexity Classes; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.2 Graph Theory; G.2.2 Network problems",
descriptor = "Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES,
Economics; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Nonlinear approximation;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Network problems",
genterm = "algorithms; theory",
guideno = "1989-12859",
source = "UMI order no: GAX89-19486",
subject = "J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL
SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY
ABSTRACT DEVICES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
DISCRETE MATHEMATICS",
}
@InProceedings{Vial:1989:APP,
author = "J.-P. Vial",
title = "Approximate projections in a projective method for the
linear feasibility problem",
crossref = "Megiddo:1989:PMP",
pages = "65--78",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74175",
bookpages = "x + 158",
catcode = "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; I.1.2 Algorithms; I.1.2
Nonalgebraic algorithms; G.1.6 Optimization; G.1.6
Constrained optimization; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations on
matrices; G.1.2 Approximation; G.1.2 Minimax
approximation and algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations; Computing
Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Optimization, Constrained
optimization; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms",
genterm = "algorithms; experimentation; measurement; performance;
theory",
guideno = "1989-12477",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{vonRosen:1989:MLE,
author = "D. von Rosen",
title = "Maximum likelihood estimators in multivariate linear
normal models",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "187--200",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Stockholm, Stockholm, Sweden",
bibno = "69314",
catcode = "G.1.6; G.1.2; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Linear approximation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Linear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; theory",
guideno = "1989-08484",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Wang:1989:SF,
author = "Z. X. Wang and D. R. Guo",
title = "Special Functions",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xiii + 422",
year = "1989",
ISBN = "9971-5-0659-9",
ISBN-13 = "978-9971-5-0659-9",
LCCN = "QA331 .W296 1989",
bibdate = "Mon Sep 3 16:10:24 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions",
}
@Article{Wasilkowski:1989:AIV,
author = "G. W. Wasilkowski",
title = "On adaptive information with varying cardinality for
linear problems with elliptically contoured measures",
journal = j-J-COMPLEXITY,
volume = "5",
number = "3",
pages = "363--368",
month = sep,
year = "1989",
CODEN = "JOCOEH",
ISSN = "0885-064X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Kentucky, Lexington, KY",
bibno = "68756",
catcode = "G.1.2; G.1.2; F.1.3",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Nonlinear
approximation; F.1.3 Complexity Classes",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Nonlinear approximation; Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes",
genterm = "algorithms; theory",
guideno = "1989-08045",
journalabbrev = "J. Complexity",
jrldate = "Sept. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES",
}
@Article{Weniger:1989:NST,
author = "Ernst Joachim Weniger",
title = "Nonlinear sequence transformations for the
acceleration of convergence and the summation of
divergent series",
journal = j-COMPUT-PHYS-REP,
volume = "10",
number = "5--6",
pages = "189--371",
month = dec,
year = "1989",
CODEN = "CPHREF",
DOI = "http://dx.doi.org/10.1016/0167-7977(89)90011-7",
ISSN = "0167-7977 (print), 1878-1004 (electronic)",
ISSN-L = "0167-7977",
bibdate = "Thu Dec 01 10:13:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Available as math.NA/0306302.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Reports",
keywords = "convergence acceleration",
}
@Article{Yortsos:1989:LSI,
author = "Y. C. Yortsos and F. J. Hickernell",
title = "Linear stability of immiscible displacement in porous
media",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "730--748",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64942",
catcode = "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Parabolic
equations; G.1.0 General; G.1.0 Stability (and
instability); J.2 Earth and atmospheric sciences; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.4 Quadrature and Numerical Differentiation; G.1.4
Finite difference methods; G.1.8 Partial Differential
Equations; G.1.8 Difference methods",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Parabolic equations;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Stability (and instability); Computer Applications,
PHYSICAL SCIENCES AND ENGINEERING, Earth and
atmospheric sciences; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation,
Finite difference methods; Mathematics of Computing,
NUMERICAL ANALYSIS, Partial Differential Equations,
Difference methods",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09711",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING",
}
@Article{Zalik:1989:NIE,
author = "R. A. Zalik",
title = "A new inequality for entire functions",
journal = j-J-APPROX-THEORY,
volume = "58",
number = "3",
pages = "281--283",
month = sep,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72294",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "verification; theory",
guideno = "1989-07871",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Ziemer:1989:WDF,
author = "William P. Ziemer",
title = "Weakly differentiable functions: {Sobolev} spaces and
functions of bounded variation",
volume = "120",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 308",
year = "1989",
ISBN = "0-387-97017-7",
ISBN-13 = "978-0-387-97017-2",
LCCN = "QA323 .Z53 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Graduate texts in mathematics",
acknowledgement = ack-nhfb,
affiliation = "Indiana Univ., Bloomington",
bibno = "69369",
catcode = "G.1.2; G.1.8; G.1.5",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.8 Partial Differential Equations;
G.1.5 Roots of Nonlinear Equations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
genterm = "algorithms; theory",
guideno = "1989-01732",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Amos:1990:RPP,
author = "Donald E. Amos",
title = "Remark on ``{Algorithm 644}: {A} Portable Package for
{Bessel} Functions of a Complex Argument and
Nonnegative Order''",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "404--404",
month = dec,
year = "1990",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/98267.98299",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:26:24 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems.",
}
@Article{Anderson:1990:FIC,
author = "G. D. Anderson and M. K. Vamanamurthy and M.
Vuorinen",
title = "Functional Inequalities for Complete Elliptic
Integrals and Their Ratios",
journal = j-SIAM-J-MATH-ANA,
volume = "21",
number = "2",
pages = "536--549",
month = mar,
year = "1990",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05 (30C62 33C75)",
MRnumber = "91d:33039",
MRreviewer = "K. C. Gupta",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Bellalij:1990:SPC,
author = "M. Bellalij",
title = "A simultaneous process for convergence acceleration
and error control",
journal = j-J-COMP-APPL-MATH,
volume = "33",
number = "2",
pages = "217--231",
day = "21",
month = dec,
year = "1990",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0377-0427(90)90370-F",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B99 (65G10)",
MRnumber = "1090897 (92a:65029)",
MRreviewer = "Thomas A. Atchison",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
keywords = "convergence acceleration",
}
@Article{Bronstein:1990:IEF,
author = "Manuel Bronstein",
title = "Integration of elementary functions",
journal = j-J-SYMBOLIC-COMP,
volume = "9",
number = "2",
pages = "117--173",
month = feb,
year = "1990",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
MRclass = "12H05 (68Q40)",
MRnumber = "91h:12017",
MRreviewer = "Alexandru Buium",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Theory/cathode.bib",
acknowledgement = ack-nhfb,
classcodes = "C1120 (Analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
Res. Center, Yorktown Heights, NY, USA",
keywords = "algebraic extension; algebraic function; decision
procedure; elementary function field; elementary
functions; exponential; finite terms; indefinite;
integration; integration Risch ODEs oderef; logarithm;
proof; Trager",
treatment = "T Theoretical or Mathematical",
}
@Article{Carre:1990:PEF,
author = "C. Carre",
title = "Plethysm of elementary functions",
journal = "Bayreuth. Math. Schr.",
volume = "31",
pages = "1--18",
year = "1990",
ISSN = "0172-1062",
MRclass = "20C30 (05E05 22E45)",
MRnumber = "91f:20013",
MRreviewer = "John R. Stembridge",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ciminiera:1990:HRS,
author = "L. Ciminiera and P. Montuschi",
title = "Higher radix square rooting",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "10",
pages = "1220--1231",
month = oct,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.59853",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
summary = "A general discussion on nonrestoring square root
algorithms is presented, showing bounds and constraints
delimiting the space of feasible algorithms, for all
the choices of radix, digit set and representation of
the partial remainder. Two classes of \ldots{}",
}
@Article{Cody:1990:PEP,
author = "W. J. Cody",
title = "Performance Evaluation of Programs for the Error and
Complementary Error Functions",
journal = j-TOMS,
volume = "16",
number = "1",
pages = "29--37",
month = mar,
year = "1990",
CODEN = "ACMSCU",
DOI = "http://dx.doi.org/10.1145/77626.77628",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65-04 (65G05)",
MRnumber = "1 073 407",
bibdate = "Tue Oct 09 09:29:47 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
abstract = "This paper presents methods for performance evaluation
of computer programs for the functions
$\textrm{erf}(x)$, $\textrm{erfc}(x)$, and $\e^{x^2}
\textrm{erfc}(x)$. Accuracy estimates are based on
comparisons using power series expansions and an
expansion in the repeated integrals of
$\textrm{erfc}(x)$. Some suggestions for checking
robustness are also given. Details of a specific
implementation of a test program are included.",
acknowledgement = ack-nhfb,
affiliation = "Argonne Nat. Lab., IL, USA",
classification = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
keywords = "Complementary error functions; Computer programs;
FORTRAN; Power series expansions; Repeated integrals;
Robustness; Test program",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
thesaurus = "Error analysis; Function approximation; Performance
evaluation",
}
@Article{Dunham:1990:FPF,
author = "C. B. Dunham",
title = "Feasibility of ``perfect'' function evaluation",
journal = j-SIGNUM,
volume = "25",
number = "4",
pages = "25--26",
month = oct,
year = "1990",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/122272.122276",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:19 MDT 2005",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
}
@Article{Dvorak:1990:NCI,
author = "Steven L. Dvorak and Edward F. Kuester",
title = "Numerical computation of the incomplete
{Lipschitz--Hankel} integral {${\rm Je}_0(a, z)$}",
journal = j-J-COMPUT-PHYS,
volume = "87",
number = "2",
pages = "301--327",
month = apr,
year = "1990",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(90)90255-Y",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:40 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199919090255Y",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Ercegovac:1990:RSR,
author = "M. D. Ercegovac and T. Lang",
title = "Radix-$4$ square root without initial {PLA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1016--1024",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.57040",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Germain-Bonne:1990:CAN,
author = "B. Germain-Bonne",
title = "Convergence acceleration of number-machine sequences",
journal = j-J-COMP-APPL-MATH,
volume = "32",
number = "1--2",
pages = "83--88",
day = "26",
month = nov,
year = "1990",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0377-0427(90)90419-Z",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B05",
MRnumber = "1091778 (91m:65007)",
MRreviewer = "W. Govaerts",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Luminy,
1989)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
keywords = "convergence acceleration",
}
@Article{Hashemian:1990:SRA,
author = "R. Hashemian",
title = "Square Rooting Algorithms for Integer and
Floating-Point Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1025--1029",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.57041",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise root is evaluated.
The major effort in this development has been
concentrated on two objectives: high speed and no
division operation other than division by 2. The first
objective is achieved through a simple two-step
procedure for getting the first estimate, and then
modifying it by employing a fast converging iteration
technique. The second objective is also fulfilled
through applying bit-shift operation rather than
division operation. The algorithm is simulated for both
integer and real numbers, and the results are compared
to two methods being widely used. The results
(tabulated) show considerable improvement in speed
compared to these other two methods.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Dept. of Electr. Eng., Northern Illinois Univ.,
Dekalb, IL, USA",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C5230
(Digital arithmetic methods)",
keywords = "Bit-shift operation; Close estimate; Division by 2;
Fast converging iteration; Floating-point numbers;
Initial value modification; Integer numbers; Precise
root; Real numbers; Square rooting algorithms",
summary = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise \ldots{}",
thesaurus = "Digital arithmetic; Iterative methods; Number theory",
}
@InProceedings{Kiernan:1990:FAE,
author = "J. M. Kiernan and T. B. Blachowiak",
title = "Fast, Accurate Elementary Functions For the {Cray
Y-MP} Computer",
crossref = "Cray:1990:PCU",
pages = "243--252",
year = "1990",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Koren:1990:EEF,
author = "I. Koren and O. Zinaty",
title = "Evaluating Elementary Functions in a Numerical
Coprocessor Based on Rational Approximations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1030--1037",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.57042",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Levrie:1990:CAN,
author = "Paul Levrie and Adhemar Bultheel",
title = "Convergence Acceleration for the Numerical Solution of
Second-Order Linear Recurrence Relations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "1",
pages = "166--177",
month = feb,
year = "1990",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
MRclass = "65Q05 (40A15 65B99)",
MRnumber = "91a:65244",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Markstein:1990:CEF,
author = "P. W. Markstein",
title = "Computation of elementary functions on the {IBM RISC
System\slash 6000} processor",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "111--119",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
MRclass = "65-04 (65D20)",
MRnumber = "1 057 659",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The additional speed and precision of the IBM RISC
System\slash 6000 floating-point unit have motivated
reexamination of algorithms to perform division, square
root, and the elementary functions. New results are
obtained which avoid the necessity of doing special
testing to get the last bit rounded correctly in
accordance with all of the IEEE rounding modes in the
case of division and square root. For the elementary
function library, a technique is described for always
getting the last bit rounded correctly in the selected
IEEE rounding mode.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Division; Elementary functions; Floating-point unit;
IBM RISC System\slash 6000 processor; IEEE rounding
modes; IEEE rounding modes, IBM RISC System/6000
processor; Square root",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@Article{Matos:1990:CAM,
author = "Ana C. Matos",
title = "A convergence acceleration method based on a good
estimation of the absolute value of the error",
journal = j-IMA-J-NUMER-ANAL,
volume = "10",
number = "2",
pages = "243--251",
year = "1990",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
MRclass = "65B99",
MRnumber = "91m:65010",
MRreviewer = "K. B{\"o}hmer",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Matula:1990:HPD,
author = "D. Matula",
title = "Highly parallel divide and square root algorithms for
a new generation floating point processor",
crossref = "Ullrich:1990:CCA",
pages = "??--??",
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Montuschi:1990:SSR,
author = "P. Montuschi and P. M. Mezzalama",
title = "Survey of square rooting algorithms",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "137",
number = "1",
pages = "31--40",
month = jan,
year = "1990",
CODEN = "ICDTEA",
ISSN = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The paper reviews the algorithms for the computation
of square roots for binary machines. After an initial
classification, the algorithms are analysed in detail
by considering their specific peculiarities and
properties. Finally, some comments are \ldots{}",
}
@InCollection{Mora:1990:EFI,
author = "Gerardo Mora and Edwin Castro and Ioan Muntean",
booktitle = "Mathematics in Costa Rica, Vol. 1 (Spanish) (San
Jos{\'e}, 1990),",
title = "Elementary functions. {I}. ({Spanish})",
publisher = "Univ. Costa Rica",
address = "San Jos{\'e}, Costa Rica",
pages = "76--86",
year = "1990",
MRclass = "26A09",
MRnumber = "1 111 714",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Muller:1990:HCA,
author = "Volker M{\"u}ller",
title = "{Hochgenaue {CORDIC}-Algorithmen f{\"u}r reelle
Standardfunktionen mittels dynamischer
Defektberechnung} \toenglish {High-accuracy {CORDIC}
Algorithms for Real Elementary Functions by Means of
Dynamic Error Computation} \endtoenglish",
type = "Diplomarbeit",
school = "Institut f{\"u}r angewandte Mathematik,
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
month = dec,
year = "1990",
bibdate = "Fri Jun 11 12:38:17 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Osada:1990:CAM,
author = "Naoki Osada",
title = "A Convergence Acceleration Method for Some
Logarithmically Convergent Sequences",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "1",
pages = "178--189",
month = feb,
year = "1990",
CODEN = "SJNAAM",
DOI = "http://dx.doi.org/10.1137/0727012",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B05",
MRnumber = "1034928 (91b:65002)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
keywords = "convergence acceleration",
}
@Article{Palmore:1990:CAC,
author = "J. Palmore and C. Herring",
title = "Computer arithmetic, chaos and fractals",
journal = j-PHYSICA-D,
volume = "42",
number = "1--3",
pages = "99--110",
month = jun,
year = "1990",
CODEN = "PDNPDT",
DOI = "http://dx.doi.org/10.1016/0167-2789(90)90069-2",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Ninth Annual International Conference of the Center
for Nonlinear Studies on Self-Organizing, Collective
and Cooperative Phenomena in Natural and Artificial
Networks",
abstract = "The authors explore aspects of computer arithmetic
from the viewpoint of dynamical systems. They
demonstrate the effects of finite precision arithmetic
in three uniformly hyperbolic chaotic dynamical
systems: Bernoulli shifts, cat maps, and pseudorandom
number generators. They show that elementary
floating-point operations in binary computer arithmetic
possess an inherently fractal structure. Each of these
dynamical systems allows us to compare the exact
results in integer arithmetic with those obtained by
using floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Illinois Univ., Urbana, IL, USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "22-26 May 1989",
conflocation = "Los Alamos, NM, USA",
keywords = "Bernoulli shifts; Binary computer arithmetic; Cat
maps; Chaos; Computer arithmetic; Dynamical systems;
Elementary floating-point operations; Finite precision
arithmetic; Floating-point arithmetic; Fractal
structure; Integer arithmetic; Pseudorandom number
generators; Self-similar structure; Uniformly
hyperbolic chaotic dynamical systems",
language = "English",
pubcountry = "Netherlands",
thesaurus = "Chaos; Digital arithmetic; Fractals; Random number
generation; Roundoff errors",
}
@Article{Sedogbo:1990:CAS,
author = "Guy Antoine Sedogbo",
title = "Convergence acceleration of some logarithmic
sequences",
journal = j-J-COMP-APPL-MATH,
volume = "32",
number = "1--2",
pages = "253--260",
day = "26",
month = nov,
year = "1990",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0377-0427(90)90435-3",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B10 (40A25 65B99)",
MRnumber = "1091794 (91m:65009)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Luminy,
1989)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
keywords = "convergence acceleration",
}
@Book{Swartzlander:1990:CA,
author = "Earl E. Swartzlander",
title = "Computer arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1990",
ISBN = "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1
microfiche)",
ISBN-13 = "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1
microfiche)",
LCCN = "QA76.6.C633 1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes.",
series = "IEEE Computer Society Press tutorial",
acknowledgement = ack-nhfb,
annote = "Vol. 1 is a reprint. Originally published:
Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
Originally published in series: Benchmark papers in
electrical engineering and computer science; 21. Vol 2
is a sequel to the earlier collection. Vol. 1: 2nd
ed.",
keywords = "Computer arithmetic.; Electronic digital computers ---
Programming.; Floating-point arithmetic.",
tableofcontents = "Arithmetic operations in a binary computer / R. F.
Shaw \\
High-speed arithmetic in binary computers / O. L.
MacSorley \\
Fast carry logic for digital computers / B. Gilchrist,
J. H. Pomerene, and S. Y. Wong \\
A logic for high-speed addition / A. Weinberger and J.
L. Smith \\
Conditional-sum addition logic / J. Sklansky \\
An evaluation of several two-summand binary adders / J.
Sklansky \\
Adder with distributed control / A. Svoboda \\
Multiple addition by residue threshold functions and
their representation by array logic / I.T. Ho and T.C.
Chen \\
Counting responders in an associative memory / C. C.
Foster and F. D. Stockton \\
Parallel counters / E. E. Swartzlander, Jr. \\
A signed binary multiplication technique / A. D. Booth
\\
Multiplying made easy for digital assemblies / C.
Ghest. A binary multiplication scheme based on squaring
/ T. C. Chen \\
A suggestion for a fast multiplier / C. S. Wallace \\
Some schemes for parallel multipliers / L. Dadda \\
On parallel digital multipliers / L. Dadda \\
A compact high-speed parallel multiplication scheme /
W. J. Stenzel, W. J. Kubitz, and G. H. Garcia \\
A two's complement parallel array multiplication
algorithm / C. R. Baugh and B. A. Wooley \\
Comments on ``A two's complement parallel array
multiplication algorithm'' / P. E. Blankenship \\
The quasi-serial multiplier / E. E. Swartzlander, Jr.
\\
The two's complement quasi-serial multiplier / T. G.
McDaneld and R. K. Guha \\
A new class of digital division methods / J. E
Robertson \\
An algorithm for rapid binary division / J. B. Wilson
and R. S. Ledley. Digit-by-digit
transcendental-function computation / R. J. Linhardt
and H. S. Miller \\
A unified algorithm for elementary functions / J. S.
Walther \\
Some properties of iterative square-rooting methods
using high-speed multiplication /C. V. Ramamoorthy, J.
R. Goodman, and K. H. Kim \\
Radix-16 evaluation of certain elementary functions /
M. D. Ercegovac \\
On the distribution of numbers / R. W. Hamming \\
An analysis of floating-point addition / D. W. Sweeney
\\
The IBM\ldots{}Model 91: floating-point execution unit
/ S. F. Anderson \ldots{} [et al.] \\
Design of large high-speed floating-point-arithmetic
units / J. B. Gosling \\
Analysis of rounding methods in floating-point
arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H.
Sameh. \\
cos x, tan-p1s x, and cot-p1s x / W. H. Specker.",
}
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title = "Accurate and Efficient Testing of the Exponential and
Logarithm Functions",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "185--200",
month = sep,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65-04 (65G99)",
MRnumber = "1 070 797",
bibdate = "Sun Sep 04 23:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/79505.79506;
http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
abstract = "Table-driven techniques can be used to test highly
accurate implementation of EXP LOG. The largest error
observed in EXP and LOG accurately to within 1/500 unit
in the last place are reported in our tests. Methods to
verify the tests' reliability are discussed. Results of
applying the tests to our own as well as to a number of
other implementations of EXP and LOG are presented.",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Certification and testing. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Portability.",
}
@TechReport{Tang:1990:PGE,
author = "Ping Tak Peter Tang",
title = "A Portable Generic Elementary Function Package in
{Ada} and an Accurate Test Suite",
type = "Technical report",
number = "ANL-90/35",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "iii + 35",
month = nov,
year = "1990",
bibdate = "Fri Dec 28 11:36:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF",
abstract = "A comprehensive set of elementary functions has been
implemented portably in Ada. The high accuracy of the
implementation has been confirmed by rigorous analysis.
Moreover, we present new test methods that are
efficient and offer a high resolution of 0.005 unit in
the last place, Tbese test methods have been
implemented portably here and confirm the accuracy of
our implemented functions. Reports on the accuracy of
other function libraries obtained by our test programs
are also presented.",
acknowledgement = ack-nhfb,
}
@TechReport{Tang:1990:SSI,
author = "Ping Tak Peter Tang",
title = "Some Software Implementations of the Functions Sine
and Cosine",
type = "Technical report",
number = "ANL-90/3",
institution = inst-ANL,
address = inst-ANL:adr,
month = apr,
year = "1990",
bibdate = "Fri Dec 28 11:21:38 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm",
abstract = "This document presents several software
implementations of the elementary functions sin and cos
designed to fit a large class of machines.
Implementation details are provided. Also provided is a
detailed error analysis that bounds the errors of these
implementations, over the full range of input
arguments, from 0.721 to 0.912 units in the last place.
Tests performed on these codes give results that are
consistent with the error bounds.",
acknowledgement = ack-nhfb,
xxnote = "Where is this? I can find no electronic version
online, other than the abstract at the given URL.",
}
@Article{Tang:1990:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Logarithm Function
in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "378--400",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Sep 04 23:26:09 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/98267.98294;
http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
abstract = "Algorithms and implementation details for the
logarithm functions in both single and double precision
of IEEE 754 arithmetic are presented here. With a table
of moderate size, the implementation need only working-
precision arithmetic and are provably accurate to
within 0.57 ulp.",
acknowledgement = ack-nj,
keywords = "algorithms; design; performance; reliability;
standardization; theory; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Article{Weniger:1990:RAM,
author = "Ernst Joachim Weniger and Ji{\v{r}}i
C{\'\i}{\v{z}}ek",
title = "Rational approximations for the modified {Bessel}
function of the second kind",
journal = j-COMP-PHYS-COMM,
volume = "59",
number = "3",
pages = "471--493",
month = jul,
year = "1990",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(90)90089-J",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:12 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/001046559090089J",
abstract = "Various different rational approximations for the
modified Bessel function $K_\nu(z)$ are compared with
respect to their ability of computing $K_\nu(z)$
efficiently and reliably in the troublesome region of
moderately large arguments $z$. The starting point for
the construction of the rational approximations is the
asymptotic series $_2F_0$ for $K_\nu(z)$, which
diverges for all finite arguments $z$ but is Borel
summable and Stieltjes summable. The numerical tests
showed that Pad{\'e} approximants for $K_\nu(z)$ are
significantly less efficient than the other rational
approximations which were considered. The best results
were produced by some recently derived sequence
transformations (E. J. Weniger, Comput. Phys. Rep. {\bf
10} (1989) 189), which are closely related to Levin's
sequence transformations (D. Levin, Int. J. Comput.
Math. B {\bf 3} (1973) 371).",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Bartoloni:1991:MFU,
author = "A. Bartoloni and C. Battista and S. Cabasino and N.
Cabibbo and F. Del Prete and F. Marzano and P. S.
Paolucci and R. Sarno and G. Salina and G. M. Todesco
and M. Torelli and R. Tripiccione and W. Tross and E.
Zanetti",
title = "{MAD}, a floating-point unit for massively-parallel
processors",
journal = "Particle World",
volume = "2",
number = "3",
pages = "65--73",
month = "????",
year = "1991",
CODEN = "PARWEG",
ISSN = "1043-6790",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The authors describe in detail the architecture and
implementation of the MAD chip. It is a floating point
unit, used as the elementary processing element of the
APE100 array processor. The design has been accurately
tailored to the requirements of a SIMD floating point
intensive machine.",
acknowledgement = ack-nhfb,
affiliation = "Roma Univ., Italy",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C7320 (Physics and
Chemistry)",
keywords = "APE100 array processor; Architecture; Elementary
processing element; Floating-point unit;
Massively-parallel processors; SIMD floating point
intensive machine",
language = "English",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Microprocessor chips; Parallel
architectures; Physics computing",
}
@InProceedings{Bohlender:1991:SEF,
author = "G. Bohlender and W. Walter and P. Kornerup and D. W.
Matula",
title = "Semantics for exact floating point operations",
crossref = "Kornerup:1991:PIS",
pages = "22--26",
year = "1991",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Catalog number 91CH3015-5.",
abstract = "Semantics are given for the four elementary arithmetic
operations and the square root, to characterize what
are termed exact floating point operations. The
operands of the arithmetic operations and the argument
of the square root are all floating point numbers in
one format. In every case, the result is a pair of
floating point numbers in the same format with no
accuracy lost in the computation. These semantics make
it possible to realize the following principle: it
shall be a user option to discard any information in
the result of a floating point arithmetic operation.
The reliability and portability previously associated
with only mathematical software implementations in
integer arithmetic can thus be attained exploiting the
generally higher efficiency of floating point
hardware.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
bookpages = "xiii + 282",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "26-28 June 1991",
conflocation = "Grenoble, France",
confsponsor = "IEEE; CNRS; IMAG",
keywords = "Argument; Elementary arithmetic operations; Exact
floating point operations; Floating point arithmetic;
Floating point hardware; Floating point numbers;
Integer arithmetic; Mathematical software; Operands;
Portability; Reliability; Semantics; Square root",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Number theory",
}
@Book{Brezinski:1991:EMT,
author = "Claude Brezinski and Michela {Redivo Zaglia}",
title = "Extrapolation methods: theory and practice",
volume = "2",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "ix + 464",
year = "1991",
ISBN = "0-444-88814-4",
ISBN-13 = "978-0-444-88814-3",
LCCN = "QA281 .B74 1991",
bibdate = "Mon May 24 09:18:52 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
series = "Studies in computational mathematics",
acknowledgement = ack-nhfb,
subject = "extrapolation; data processing",
}
@Article{Bunch:1991:DFA,
author = "K. J. Bunch and W. N. Cain and R. W. Grow",
title = "A data fitting approach to series convergence
acceleration",
journal = j-APPL-MATH-COMP,
volume = "42",
number = "2 (part II)",
pages = "189--195",
month = "????",
year = "1991",
CODEN = "AMHCBQ",
DOI = "http://dx.doi.org/10.1016/0096-3003(91)90050-W",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65B10 (65D10)",
MRnumber = "1094414 (91k:65015)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
keywords = "convergence acceleration",
}
@Article{Carlson:1991:TEI,
author = "B. C. Carlson",
title = "A table of elliptic integrals: {One} quadratic
factor",
journal = j-MATH-COMPUT,
volume = "56",
number = "193",
pages = "267--280",
month = jan,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33E05 (65A05)",
MRnumber = "92b:33056",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); B0290M (Numerical
integration and differentiation); C4180 (Integral
equations); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
keywords = "conjugate complex zeros; elliptic integrals; Fortran
programs; integral equations; integration; polynomial;
R-functions; square root",
treatment = "P Practical",
}
@TechReport{Cody:1991:CPT,
author = "W. J. Cody",
title = "{CELEFUNT}: {A} Portable Test Package for Complex
Elementary Functions",
type = "Technical Report",
number = "ANL-91/1",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "iii + 21",
month = jan,
year = "1991",
bibdate = "Fri Sep 23 23:39:07 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Corless:1991:NEA,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "93",
number = "1",
pages = "252--253",
month = mar,
year = "1991",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(91)90089-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:47 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999191900894",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Crenshaw:1991:SRS,
author = "J. W. Crenshaw",
title = "Square roots are simple?",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "11",
pages = "30--52",
month = nov,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Wed Sep 14 19:14:52 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dritz:1991:IPS,
author = "Kenneth W. Dritz",
title = "Introduction to the proposed standard for the
elementary functions in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "3--8",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics)",
corpsource = "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
IL, USA",
keywords = "Ada; committees; elementary functions; generic
package; ISO standard; mathematics computing;
secondary; standards",
treatment = "P Practical",
}
@Article{Dritz:1991:PSGa,
author = "K. W. Dritz",
title = "Proposed standard for a generic package of elementary
functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "9--46",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C6110B (Software
engineering techniques); C7310 (Mathematics)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
keywords = "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
Working Group; basic; elementary functions;
ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
GENERIC-ELEMENTARY-FUNCTIONS; Group; international
standard; joint proposal; mathematical routines;
mathematics computing; NRG; Rapporteur Group; reusable
applications; SC22; software reusability;
specification; standards; WG9 Numerics",
treatment = "P Practical",
}
@Article{Dritz:1991:PSGb,
author = "K. W. Dritz",
title = "Proposed standard for a generic package of primitive
functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "66--82",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
keywords = "Ada; compliable Ada; elementary functions; generic
package; GENERIC-; mathematical; mathematics computing;
primitive functions; primitive operations;
PRIMITIVE-FUNCTIONS; software; specification;
standards",
treatment = "P Practical",
}
@Article{Dritz:1991:RPS,
author = "K. W. Dritz",
title = "Rationale for the proposed standard for a generic
package of elementary functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "47--65",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110 (Systems analysis and programming)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
Numerics; collateral; elementary functions standard;
mathematics computing; numerical software; portability;
programming; robustness; standards; Working Group",
treatment = "P Practical",
}
@Article{Duprat:1991:WND,
author = "J. Duprat and J.-M. Muller",
title = "Writing numbers differently for faster calculation",
journal = j-TECHNIQUE-SCI-INFORMATIQUES,
volume = "10",
number = "3",
pages = "211--224",
month = "????",
year = "1991",
CODEN = "TTSIDJ",
ISSN = "0752-4072, 0264-7419",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Instead of Avizienis' or the carry save methods a
borrow save (BS) notation is proposed. Examples are
given of BS addition, subtraction, shifting and
multiplication with the necessary elementary cells
being proposed and circuits for testing zero and sign
being described. Floating point arithmetic is
explained, involving pseudo normalisation and
applications are covered including the Cordic
algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Addition; Borrow save; Carry save methods; Cordic
algorithm; Floating point arithmetic; Multiplication;
Pseudo normalisation; Shifting; Subtraction; Zero",
language = "French",
pubcountry = "France",
thesaurus = "Digital arithmetic",
}
@InProceedings{Ferguson:1991:AMA,
author = "W. E. {Ferguson, Jr.} and T. Brightman",
title = "Accurate and Monotone Approximations of Some
Transcendental Functions",
crossref = "Kornerup:1991:PIS",
pages = "237--244",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "26--45",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20 (65-04 65D15)",
MRnumber = "92a:65069",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
abstract = "The algorithms used by the IBM Israel Scientific
Center for the elementary mathematical library using
the IEEE standard for binary floating point arithmetic
are described. The algorithms are based on the
``accurate tables method.'' This methodology achieves
high performance and produces very accurate results. It
overcomes one of the main problems encountered in
elementary mathematical functions computations:
achieving last bit accuracy. The results obtained are
correctly rounded for almost all argument values.
\par
Our main idea in the accurate tables method is to use
``nonstandard tables,'' which are different from the
natural tables of equally spaced points in which the
rounding error prevents obtaining last bit accuracy. In
order to achieve a small error we use the following
idea: Perturb the original, equally spaced, points in
such a way that the table value (or tables values in
case we need several tables) will be very close to
numbers which can be exactly represented by the
computer (much closer than the usual double precision
representation). Thus we were able to control the error
introduced by the computer representation of real
numbers and extended the accuracy without actually
using extended precision arithmetic.",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation.",
}
@InProceedings{Gustafson:1991:CAA,
author = "Sven-{\AA}ke Gustafson and Frank Stenger",
title = "Convergence acceleration applied to {Sinc}
approximation with application to approximation of
$|x|^\alpha$",
crossref = "Bowers:1991:CCI",
pages = "161--171",
year = "1991",
MRclass = "41A30 (93B40)",
MRnumber = "MR1140021",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The author studies mainly the role of Chebyshev
acceleration of Sinc approximation. Then he considers
various methods of approximating $\vert x\vert^ \alpha$
and applies Chebyshev acceleration to the various type
of approximants for the case of $\alpha=1$.",
acknowledgement = ack-nhfb,
classmath = "*41A65 (Abstract approximation theory)",
keywords = "Chebyshev acceleration; convergence acceleration",
reviewer = "Zhang Ganglu (Dongying)",
ZMnumber = "0746.41034",
}
@Article{Hamza:1991:MBD,
author = "K. M. Hamza and M. A. H. Abdul-Karim",
title = "Microprocessor Based Direct Square Root Extractor",
journal = "Modelling",
volume = "34",
number = "1",
pages = "45--48",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Iserles:1991:CDC,
author = "A. Iserles",
title = "Complex dynamics of convergence acceleration",
journal = j-IMA-J-NUMER-ANAL,
volume = "11",
number = "2",
pages = "205--240",
year = "1991",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
MRclass = "65B05 (65E05)",
MRnumber = "92h:65006",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Levrie:1991:CAF,
author = "Paul Levrie",
title = "Convergence acceleration for $n$-fractions",
journal = j-APPL-NUM-MATH,
volume = "7",
number = "6",
pages = "481--492",
month = jun,
year = "1991",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "40A15 (65B05)",
MRnumber = "92k:40001",
MRreviewer = "Claude Brezinski",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Levrie:1991:CFC,
author = "Paul Levrie",
title = "${G}$-continued fractions and convergence acceleration
in the solution of third-order linear recurrence
relations of {Poincar{\'e}} type",
journal = j-APPL-NUM-MATH,
volume = "8",
number = "3",
pages = "225--242",
month = oct,
year = "1991",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "65B99 (65Q05)",
MRnumber = "92m:65012",
MRreviewer = "J. Albrycht",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Lyons:1991:FMF,
author = "Ken Lyons",
title = "A fast method for finding an integer square root",
crossref = "Koopman:1991:PST",
pages = "27--30",
year = "1991",
bibdate = "Tue May 4 05:57:50 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
acknowledgement = ack-nhfb,
}
@InProceedings{Markstein:1991:WFF,
author = "V. Markstein and P. Markstein and T. Nguyen and S.
Poole",
title = "Wide Format Floating-Point Math Libraries",
crossref = "IEEE:1991:PSA",
pages = "130--138",
year = "1991",
bibdate = "Wed Dec 13 18:34:51 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The authors present the performance and accuracy
evaluations of eleven transcendental functions found in
64- and 128-bit floating-point formats in math
libraries on the Cray Y-MP, the IBM 3090E/VF, the
Convex C-240, the Hewlett--Packard 9000/720, and the
IBM System/6000. Both architecture and algorithms are
shown to impact the results.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "ISQUARE, Inc., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing); C7310
(Mathematics)",
confdate = "18-22 Nov. 1991",
conflocation = "Albuquerque, NM, USA",
confsponsor = "IEEE; ACM",
keywords = "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
Cray Y-MP; Floating-point formats; Hewlett--Packard
9000/720; IBM 3090E/VF; IBM System/6000; Math
libraries; Performance; Transcendental functions; Wide
format floating point math libraries",
language = "English",
numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Mathematics computing; Parallel
processing; Performance evaluation",
}
@Article{Maximon:1991:EIP,
author = "Leonard C. Maximon",
title = "On the evaluation of the integral over the product of
two spherical {Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "32",
number = "3",
pages = "642--648",
month = mar,
year = "1991",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.529405",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33C55",
MRnumber = "92f:33018",
MRreviewer = "S. K. Chatterjea",
bibdate = "Tue Nov 1 08:57:23 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1",
acknowledgement = ack-nhfb,
pagecount = "7",
}
@Article{McQuillan:1991:HPV,
author = "S. E. McQuillan and J. V. McCanny and R. F. Woods",
title = "High performance {VLSI} architecture for division and
square root",
journal = j-ELECT-LETTERS,
volume = "27",
number = "1",
pages = "19--21",
day = "3",
month = jan,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A novel high performance bit parallel architecture to
perform square root and division is proposed. Relevant
VLSI design issues have been addressed. By employing
redundant arithmetic and a semisystolic schedule, the
throughput has been made \ldots{}",
}
@InProceedings{McQuillan:1991:VAM,
author = "S. E. McQuillan and J. V. McCanny",
booktitle = "1991 International Conference on Acoustics, Speech,
and Signal Processing: ICASSP-91, 14--17 April 1991",
title = "A {VLSI} architecture for multiplication, division and
square root",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1205--1208",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A high-performance VLSI architecture to perform
combined multiply-accumulate, divide, and square root
operations is proposed. The circuit is highly regular,
requires only minimal control, and can be reconfigured
for every cycle. The execution time \ldots{}",
}
@Article{Midy:1991:CSE,
author = "P. Midy and Y. Yakovlev",
title = "Computing some elementary functions of a complex
variable",
journal = j-MATH-COMP-SIM,
volume = "33",
number = "1",
pages = "33--49",
year = "1991",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
MRclass = "65Y10 (65D20)",
MRnumber = "MR1122989",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
}
@Article{Montuschi:1991:OAE,
author = "P. Montuschi and M. Mezzalama",
title = "Optimal Absolute Error Starting Values for
{Newton--Raphson} Calculation of Square Root",
journal = j-COMPUTING,
volume = "46",
number = "1",
pages = "67--86",
month = mar,
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H05 (65G99)",
MRnumber = "92a:65161",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
affiliation = "Politecnico di Torino",
affiliationaddress = "Torino, Italy",
classification = "723; 921",
fjournal = "Computing",
journalabr = "Comput Vienna New York",
keywords = "Absolute Error; Computer Programming --- Algorithms;
Mathematical Techniques; Newton--Raphson Method;
Optimization; Square Roots",
}
@InProceedings{Montuschi:1991:SRD,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "Simple radix 2 division and square root with skipping
of some addition steps",
crossref = "Kornerup:1991:PIS",
pages = "202--209",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
summary = "The authors present a novel algorithm for shared radix
2 division and square root whose main characteristic is
the ability to avoid any addition when the digit 0 has
been selected. The solution presented uses a redundant
representation of the \ldots{}",
}
@Article{OGrady:1991:HOA,
author = "E. Pearse O'Grady and Baek-Kyu Young",
title = "A hardware-oriented algorithm for floating-point
function generation",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "237--241",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.73596",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "An algorithm is presented for performing accurate,
high-speed, floating-point function generation for
univariate functions defined at arbitrary breakpoints.
Rapid identification of the breakdown interval, which
includes the input argument, is the key operation in
the algorithm. A hardware implementation which makes
extensive use of read/write memories illustrates the
algorithm.",
acknowledgement = ack-nhfb,
}
@Article{Okabe:1991:LDC,
author = "Y. Okabe and N. Takagi and S. Yaima",
key = "OTY91",
title = "Log-Depth Circuits for Elementary Functions Using
Residue Number System",
journal = j-ELECTRON-COMMUN-JPN,
volume = "74",
number = "8",
pages = "31--37",
year = "1991",
CODEN = "ECOJAL",
ISSN = "0424-8368",
bibdate = "Mon May 19 15:16:09 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
acknowledgement = ack-nhfb,
}
@Article{Olver:1991:UEIb,
author = "F. W. J. Olver",
title = "Uniform, Exponentially Improved, Asymptotic Expansions
for the Confluent Hypergeometric Function and Other
Integral Transforms",
journal = j-SIAM-J-MATH-ANA,
volume = "22",
number = "5",
pages = "1475--1489",
month = sep,
year = "1991",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "41A60 (33C15)",
MRnumber = "92g:41035",
MRreviewer = "Hans-J{\"u}rgen Glaeske",
bibdate = "Sun Nov 28 19:25:21 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
}
@Book{Saan:1991:VFP,
author = "T. Saan",
title = "{\cyr Vychislenie {\`e}lementarnykh funktsi{\u{\i}}s
pomoshch'yu drobno-ratsional'nykh priblizheni{\u{\i}}}.
({Russian}) [Calculation of elementary functions by
means of rational approximations]",
publisher = "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
Tekhn. Inform., Tartu,",
pages = "139",
year = "1991",
MRclass = "65-04 (65D15)",
MRnumber = "94f:65008",
MRreviewer = "W. Govaerts",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Smith:1991:AFP,
author = "David M. Smith",
title = "Algorithm 693: {A FORTRAN} Package for Floating-Point
Multiple-Precision Arithmetic",
journal = j-TOMS,
volume = "17",
number = "2",
pages = "273--283",
month = jun,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Sep 04 23:44:20 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
abstract = "FM is a collection of FORTRAN-77 routines which
performs floating-point multiple-precision arithmetic
and elementary functions. Results are almost always
correctly rounded, and due to improved algorithms used
for elementary functions, reasonable efficiency is
obtained.",
acknowledgement = ack-nhfb,
affiliation = "Loyola Marymount Univ., Los Angeles, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310
(Mathematics)",
keywords = "Accuracy; Algorithms; Elementary functions;
Floating-point multiple-precision arithmetic; FM;
FORTRAN-77 routines; Mathematical library; Portable
software; Rounding off",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Digital arithmetic; Function approximation;
Mathematics computing; Software packages; Subroutines",
}
@Article{Squire:1991:ANS,
author = "Jon S. Squire",
title = "{Ada} numerics standardization and testing",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
address = "New York, NY, USA",
pages = "1--286",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "``A special edition from SIGAda \ldots{} presented by
SIGAda Numerics Working Group and Ada-Europe Numerics
Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
Rapporteur Group.''--Cover. Includes bibliographies.
Introduction to the proposed standard for the
elementary functions in Ada / Kenneth W. Dritz ---
Proposed standard for a generic package of elementary
functions for Ada / edited by Kenneth W. Dritz ---
Rationale for the proposed standard for a generic
package of elementary functions for Ada; Proposed
standard for a generic package of primitive functions
for Ada; Rationale for the proposed standard for a
generic package of primitive functions for Ada /
Kenneth W. Dritz --- Proposed standard for packages of
real and complex type declarations and basic operations
for Ada (including vector and matrix types) / edited by
Graham S. Hodgson --- Rationale for the proposed
standard for packages of real and complex type
declarations and basic operations for Ada (including
vector and matrix types) / Graham S. Hodgson. Proposed
standard for a generic package of complex elementary
functions / edited by Jon S. Squire --- Rationale for
the proposed standard for a generic package of complex
elementary functions / Jon S. Squire --- A portable
generic elementary function package in Ada and an
accurate test suite / Ping Tak Peter Tang --- Towards
validation of generic elementary functions and other
standard Ada numerics packages / Jon S. Squire ---
Floating point attributes in Ada / Dik T. Winter --- An
Ada math library for real-time avionics / Donald A.
Celarier and Donald W. Sando --- Predifined floating
point type names, uniformity rapporteur group UI-48 /
edited by Jon S. Squire.",
keywords = "Ada (Computer program language)",
}
@Article{Squire:1991:PSG,
author = "J. S. Squire",
title = "Proposed standard for a generic package of complex
elementary functions (Ada)",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "140--165",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110B (Software engineering techniques)",
keywords = "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
applications; complex elementary functions; complex
mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS;
generic package; GENERIC-; international standard;
joint proposal; mathematics computing; Numerics Working
Group; portable; reusable; software reusability;
standards; WG9 Numerics Rapporteur Group",
treatment = "P Practical",
}
@Article{Squire:1991:RPS,
author = "J. S. Squire",
title = "Rationale for the proposed standard for a generic
package of complex elementary functions (Ada)",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "166--179",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110B (Software engineering techniques)",
keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
complex mathematical; complex;
COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
error bounds; Europe Numerics Working Group; generic
package; GENERIC-; mathematics computing; proposed
standard; reusable applications; routines; software
reusability; specification; standards",
treatment = "P Practical",
}
@Article{Squire:1991:TVG,
author = "J. S. Squire",
title = "Towards validation of generic elementary functions and
other standard {Ada} numerics packages",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "217--243",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6150G (Diagnostic, testing, debugging and evaluating
systems); C7310 (Mathematics); C6140D (High level
languages)",
keywords = "Ada; Ada listings; computing; conformance testing;
conformance tests; generic elementary functions;
implementors guide; mathematics; program testing;
proposed ISO; prototype tests; standard Ada numerics
packages; standards; test suite",
treatment = "P Practical",
}
@Article{Tang:1991:PGE,
author = "Ping Tak Peter Tang",
title = "A portable generic elementary function package in
{Ada} and an accurate test suite",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "181--216",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C6140D (High level languages);
C6110B (Software engineering techniques); C6150G
(Diagnostic, testing, debugging and evaluating
systems)",
keywords = "accurate test; Ada; function libraries; mathematics
computing; portability; portable generic elementary
function package; program testing; resolution; rigorous
analysis; software; suite; test programs",
treatment = "P Practical",
}
@InProceedings{Tang:1991:TLA,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
crossref = "Kornerup:1991:PIS",
pages = "232--236",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@InProceedings{Wong:1991:FHA,
author = "W. F. Wong and E. Goto",
title = "Fast Hardware-based Algorithms for Elementary Function
Computations",
crossref = "Anonymous:1991:PIS",
pages = "56--65",
year = "1991",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
searchkey = "ti:elementary function",
}
@Article{Zeilberger:1991:MPP,
author = "Doron Zeilberger",
title = "A {Maple} program for proving hypergeometric
identities",
journal = j-SIGSAM,
volume = "25",
number = "3",
pages = "4--13",
month = jul,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
bibdate = "Fri Feb 8 18:27:01 MST 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Gives the listing of a MAPLE program for implementing
an algorithm for proving any terminating definite
hypergeometric identity, and more generally, for
finding the linear recurrence satisfied by any definite
hypergeometric sum R(n):= Sigma /sub k/F(n,k), where
F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/(
alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub
i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub
i'/)!). The algorithm for definite hypergeometric
summation relies on Gosper's (1978) ingenious decision
procedure for indefinite summation, but not in the
obvious way!.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
classcodes = "C7310 (Mathematics)",
classification = "C7310 (Mathematics)",
corpsource = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
issue = "97",
keywords = "definite; Definite hypergeometric summation;
hypergeometric identity; hypergeometric summation;
linear recurrence; Linear recurrence; manipulation;
MAPLE program; mathematics computing; proofs; Proofs;
public domain software; shareware; Shareware; symbol;
terminating definite; Terminating definite
hypergeometric identity; theorem proving",
thesaurus = "Mathematics computing; Public domain software; Symbol
manipulation; Theorem proving",
treatment = "P Practical",
}
@Article{Ziv:1991:FEE,
author = "Abraham Ziv",
title = "Fast Evaluation of Elementary Mathematical Functions
with Correctly Rounded Last Bit",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "410--423",
month = sep,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
acknowledgement = ack-nj,
keywords = "algorithms; standardization; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency.",
}
@Article{Anderson:1992:FIH,
author = "G. D. Anderson and M. K. Vamanamurthy and M.
Vuorinen",
title = "Functional Inequalities for Hypergeometric Functions
and Complete Elliptic Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "23",
number = "2",
pages = "512--524",
month = mar,
year = "1992",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33C05 (33C75)",
MRnumber = "93b:33001",
MRreviewer = "J. M. H. Peters",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Baker:1992:CMF,
author = "Louis Baker",
title = "{C} mathematical function handbook",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xviii + 757",
year = "1992",
ISBN = "0-07-911158-0",
ISBN-13 = "978-0-07-911158-6",
LCCN = "QA351.B17 1991; QA351 .B17 1992",
bibdate = "Fri Aug 31 18:54:02 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
series = "McGraw-Hill programming tools for scientists and
engineers",
acknowledgement = ack-nhfb,
remark = "System requirements for computer disk: PC; C or C++
compiler.",
subject = "Functions, Special; Computer programs; C (Computer
program language)",
}
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary Functions",
journal = j-SIGPLAN,
volume = "27",
number = "11",
pages = "15--16",
month = nov,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Sep 08 08:11:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Article{Bohman:1992:FRP,
author = "Jan Bohman and Carl-Erik Fr{\"o}berg",
title = "The ${\Gamma}$-function revisited: power series
expansions and real-imaginary zero lines",
journal = j-MATH-COMPUT,
volume = "58",
number = "197",
pages = "315--322",
month = jan,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33B15 (11Y70 65D20)",
MRnumber = "92e:33001",
MRreviewer = "A. de Castro Brzezicki",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Borwein:1992:FEG,
author = "J. M. Borwein and I. J. Zucker",
title = "Fast evaluation of the gamma function for small
rational fractions using complete elliptic integrals of
the first kind",
journal = j-IMA-J-NUMER-ANAL,
volume = "12",
number = "4",
pages = "519--526",
year = "1992",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D20",
MRnumber = "93g:65028",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Buhring:1992:GHF,
author = "Wolfgang B{\"u}hring",
title = "Generalized hypergeometric functions at unit
argument",
journal = j-PROC-AM-MATH-SOC,
volume = "114",
number = "1",
pages = "145--153",
month = "????",
year = "1992",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "33C20",
MRnumber = "MR1068116 (92c:33004)",
bibdate = "Thu Dec 01 09:52:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
remark = "The paper treats $_{p+1}F_p$ (or equivalently, $_pF_{p
- 1}$).",
ZMnumber = "Zbl 0754.33003",
}
@Article{Carlson:1992:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals: Two Quadratic Factors",
journal = j-MATH-COMPUT,
volume = "59",
number = "199",
pages = "165--180",
month = jul,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D20 (33C75 33E05)",
MRnumber = "92k:65027",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Corless:1992:NEAa,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "98",
number = "2",
pages = "347--347",
month = feb,
year = "1992",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(92)90150-W",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:53 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290150W",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Corless:1992:NEAb,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "99",
number = "1",
pages = "106--114",
month = mar,
year = "1992",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(92)90279-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "65D20 (33E30)",
MRnumber = "92k:65028",
bibdate = "Mon Jan 2 07:55:54 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/0021999192902798",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
keywords = "Maple",
}
@Article{Croft:1992:ACA,
author = "A. Croft",
title = "An application of convergence acceleration techniques
to a class of two-point boundary value problems on a
semi-infinite domain",
journal = j-NUMER-ALGORITHMS,
volume = "2",
number = "3--4",
pages = "307--320",
month = sep,
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
MRclass = "65L10 (65B99)",
MRnumber = "93g:65097",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
corpsource = "Dept. of Math. Sci., Leicester Polytech., UK",
keywords = "boundary condition; boundary-value problems;
convergence acceleration; convergence acceleration
algorithms; convergence of numerical methods;
extrapolate; extrapolation; semi-infinite domain;
two-point boundary value problems; unbounded domains",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Dattoli:1992:GFM,
author = "G. Dattoli and C. Chiccoli and S. Lorenzutta and G.
Maino and M. Richetta and A. Torre",
title = "Generating functions of multivariable generalized
{Bessel} functions and {Jacobi}-elliptic functions",
journal = j-J-MATH-PHYS,
volume = "33",
number = "1",
pages = "25--36",
month = jan,
year = "1992",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.529959",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33E05 (33C10 34B30 42A16 42A85)",
MRnumber = "92m:33037",
MRreviewer = "J. M. H. Peters",
bibdate = "Tue Nov 1 08:57:37 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v33/i1/p25_s1",
acknowledgement = ack-nhfb,
pagecount = "12",
}
@Article{DiDonato:1992:ASD,
author = "Armido R. {DiDonato} and Alfred H. {Morris, Jr.}",
title = "{Algorithm 708}: Significant Digit Computation of the
Incomplete Beta Function Ratios",
journal = j-TOMS,
volume = "18",
number = "3",
pages = "360--373",
month = sep,
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Nov 19 13:14:47 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Brown:1994:CAS}.",
URL = "http://doi.acm.org/10.1145/131766.131776;
http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/",
abstract = "An algorithm is given for evaluating the incomplete
beta function ratio $I_{x}(a,b)$ and its complement $1
- I^{x}(a,b)$. A new continued fraction and a new
asymptotic series are used with classical results. A
transportable Fortran subroutine based on this
algorithm is currently in use. It is accurate to 14
significant digits when precision is not restricted by
inherent error.",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation.",
}
@InProceedings{Dubois:1992:CFQ,
author = "D. Dubois and H. Prade",
title = "Calculation with fuzzy quantities",
crossref = "EC2:1992:DJN",
pages = "24--27",
year = "1992",
bibdate = "Thu Dec 14 17:22:18 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In some instances where numerical data are either
provisional, incomplete, or variable within a limited
range, the classical calculation of confidence
intervals can be extended in a fuzzy-set approach,
distinguishing between more or less plausible values.
The simultaneous use of relatively wide intervals
containing all possible values, and generally much
narrower intervals covering only the most likely ones,
can give sufficiently informative results. Some
precautions advisable in arithmetic operations on
imprecisely known quantities are outlined. Examples of
application include provisional budgeting, resource
estimation, evaluation of candidates, and extension of
PERT to projects involving precedence among elementary
tasks with uncertain durations and/or starting times.
Computer-aided engineering design can also benefit from
fuzzy specifications for values eventually to be
optimised.",
acknowledgement = ack-nhfb,
affiliation = "IRIT, Paul Sabatier Univ., Toulouse, France",
bookpages = "384",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C7310 (Mathematics)",
confdate = "2-3 Nov. 1992",
conflocation = "Nimes, France",
keywords = "Arithmetic operations; Candidates; Confidence
intervals; Engineering design; Fuzzy quantities; Fuzzy
specifications; Fuzzy-set approach; Imprecisely known
quantities; Numerical data; PERT; Provisional
budgeting; Resource estimation",
language = "French",
pubcountry = "France",
thesaurus = "Fuzzy logic; Fuzzy set theory; Statistical analysis",
}
@Article{Feinsilver:1992:BFR,
author = "P. Feinsilver and R. Schott",
title = "On {Bessel} functions and rate of convergence of zeros
of {Lommel} polynomials",
journal = j-MATH-COMPUT,
volume = "59",
number = "199",
pages = "153--156",
month = jul,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33C10 (33C45)",
MRnumber = "93a:33007",
MRreviewer = "Boro D{\"o}ring",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
affiliation = "Southern Illinois Univ., Carbondale, IL, USA",
classcodes = "B0220 (Analysis); B0290P (Differential equations);
B0290F (Interpolation and function approximation);
B0210 (Algebra); C1120 (Analysis); C4170 (Differential
equations); C4130 (Interpolation and function
approximation); C1110 (Algebra)",
classification = "B0210 (Algebra); B0220 (Analysis); B0290F
(Interpolation and function approximation); B0290P
(Differential equations); C1110 (Algebra); C1120
(Analysis); C4130 (Interpolation and function
approximation); C4170 (Differential equations)",
corpsource = "Southern Illinois Univ., Carbondale, IL, USA",
keywords = "average case analysis; Average case analysis; Bessel
function; Bessel functions; convergence of numerical
methods; convergence rate; Convergence rate; data
structures; differential equations; dynamic; Dynamic
data structures; Lommel; Lommel polynomials; Maple
program; polynomials; rate of convergence; Rate of
convergence; zeros; Zeros",
thesaurus = "Bessel functions; Convergence of numerical methods;
Differential equations; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{Kearfott:1992:IPF,
author = "Baker Kearfott and Milind Dawande and Kaisheng Du and
Chen-Yi Hu",
title = "{INTLIB}: {A} Portable {FORTRAN} 77 Elementary
Function Library",
journal = j-INTERVAL-COMP,
volume = "3",
number = "5",
pages = "96--105",
year = "1992",
ISSN = "0135-4868",
MRclass = "65G10",
MRnumber = "1 253 132",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Interval '92 (Moscow, 1992).",
acknowledgement = ack-nhfb,
}
@Article{Kzaz:1992:CAS,
author = "M. Kzaz",
title = "Convergence acceleration of some {Gaussian} quadrature
formulas for analytic functions",
journal = j-APPL-NUM-MATH,
volume = "10",
number = "6",
pages = "481--496",
month = nov,
year = "1992",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "65B10 (65D32)",
MRnumber = "93j:65004",
MRreviewer = "J. Kofro{\v{n}}",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Lang:1992:HRS,
author = "T. Lang and P. Montuschi",
title = "Higher radix square root with prescaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "996--1009",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.156542",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A scheme for performing higher radix square root based
on prescaling of the radicand is presented to reduce
the complexity of the result-digit selection. The
scheme requires several steps, namely multiplication
for prescaling the radicand, square \ldots{}",
}
@InProceedings{Liu:1992:QBS,
author = "K. J. R. Liu and E. Frantzeskakis",
booktitle = "Workshop on VLSI Signal Processing, V, 1992",
title = "Qrd-based Square Root Free and Division Free
Algorithms and Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "459--468",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Misc{Lynch:1992:HSD,
author = "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
T. Hurson",
title = "High speed divider with square root capability",
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,128,891.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Martin:1992:TPQa,
author = "Pablo Martin and Ricardo P{\'e}rez and Antonio L.
Guerrero",
title = "Two-point quasi-fractional approximations to the
{Airy} function {${\rm Ai}(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "98",
number = "2",
pages = "349--349",
month = feb,
year = "1992",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(92)90165-U",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:53 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290165U",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Martin:1992:TPQb,
author = "Pablo Mart{\'\i}n and Ricardo P{\'e}rez and Antonio L.
Guerrero",
title = "Two-point quasi-fractional approximations to the
{Airy} function {${\rm Ai}(x)$}",
journal = j-J-COMPUT-PHYS,
volume = "99",
number = "2",
pages = "337--340",
month = apr,
year = "1992",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1016/0021-9991(92)90212-H",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:55 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290212H",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Matos:1992:CAP,
author = "Ana C. Matos",
title = "Convergence and acceleration properties for the vector
$\epsilon$-algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "3",
number = "1--4",
pages = "313--319",
month = dec,
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
MRclass = "65B99",
MRnumber = "93h:65006",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Puerto de la
Cruz, 1992).",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
conflocation = "Puerto de la Cruz, Spain; 13-17 Jan. 1992",
conftitle = "International Mathematical Congress on Extrapolation
and Rational Approximation",
corpsource = "Fac. de Ciencias, Porto Univ., Portugal",
keywords = "acceleration; convergence acceleration; convergence of
numerical methods; convergence speed; exactness;
extrapolation; extrapolation algorithm; speed of
convergence; vector $\epsilon$-algorithm; vector
sequences",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{McQuillan:1992:VMH,
author = "S. E. McQuillan and J. V. McCanny",
title = "{VLSI} module for high-performance multiply, square
root and divide",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "6",
pages = "505--510",
month = nov,
year = "1992",
CODEN = "ICDTEA",
ISSN = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A high-performance VLSI architecture to perform
multiply-accumulate, division and square root
operations is proposed. The circuit is highly regular,
requires only minimal control and ean be pipelined
right down to the bit level. The system can also
\ldots{}",
}
@Article{Mikami:1992:NDO,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "A New {DSP}-Oriented Algorithm for Calculation of the
Square Root Using a Nonlinear Digital Filter",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "7",
pages = "1663--1669",
month = jul,
year = "1992",
CODEN = "ITPRED",
DOI = "http://dx.doi.org/10.1109/78.143438",
ISSN = "1053-587X",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
summary = "A high-speed algorithm for calculating the square root
is proposed. This algorithm, which can be regarded as
calculation of the step response of a kind of nonlinear
IIR filter, requires no divisions. Therefore, it is
suitable for a VLSI digital \ldots{}",
}
@Article{Mitchell:1992:VFA,
author = "H. B. Mitchell",
title = "Very fast accurate square-root algorithm for use with
gradient edge operators",
journal = j-ELECT-LETTERS,
volume = "28",
number = "10",
pages = "922--923",
day = "7",
month = may,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Commonly used gradient edge operators such as the
Sobel, Prewitt and Roberts operators all required a
square root operation; this is, however,
computationally intensive and, consequently, simple but
very inaccurate approximations are often used
\ldots{}",
}
@Article{Paszkowski:1992:CAC,
author = "Stefan Paszkowski",
title = "Convergence acceleration of continued fractions of
{Poincar{\'e}}'s type $1$",
journal = j-NUMER-ALGORITHMS,
volume = "2",
number = "2",
pages = "155--170",
month = "????",
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
MRclass = "65B05 (40A15)",
MRnumber = "93c:65006",
MRreviewer = "A. Bultheel",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Instytut Niskich Temp. i Badan Strukturalnych PAN,
Wroclaw, Poland",
keywords = "asymptotic behaviour; continued fractions; convergence
acceleration; convergence of numerical methods;
function approximation",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Salwin:1992:UPE,
author = "A. E. Salwin",
title = "Using the Proposed Elementary Functions Standard to
Build a Strongly Typed Trig Package",
journal = j-SIGADA-LETTERS,
volume = "12",
number = "5",
pages = "59--63",
month = sep # "\slash " # oct,
year = "1992",
CODEN = "AALEE5",
ISSN = "0736-721X",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages)",
corpsource = "Mitre Corp., McLean, VA, USA",
keywords = "Ada; compiler; elementary functions standard;
standards; strong typing; strongly typed trig package;
trigonometric functions",
treatment = "P Practical",
}
@MastersThesis{Schulte:1992:AHD,
author = "Michael Joseph Schulte and Function generation",
title = "Algorithms and hardware designs for parallel
elementary function generation",
type = "Thesis (M.S. in Engin.)",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "ix + 73",
year = "1992",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment -- Design and
construction.; Computer science -- Mathematics.;
Numerical analysis.; Parallel processing (Electronic
computers)",
searchkey = "ti:elementary n1 function",
}
@Article{Tang:1992:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the {{\tt Expm1}}
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "211--222",
month = jun,
year = "1992",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/146847.146928",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D15",
MRnumber = "1 167 891",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See independent analysis and accuracy confirmation of
this algorithm in \cite{Kramer:1998:PWC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
abstract = "Algorithms and implementation details for the function
$e^x - 1$ in both single and double precision of IEEE
754 arithmetic are presented here. With a table of
moderate size, the implementations need only
working-precision arithmetic and are provably accurate
to within 0.58 ulp.",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Article{Temme:1992:AII,
author = "N. M. Temme",
title = "Asymptotic Inversion of Incomplete Gamma Functions",
journal = j-MATH-COMPUT,
volume = "58",
number = "198",
pages = "755--764",
month = apr,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33B20",
MRnumber = "93a:33003",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Wong:1992:DSR,
author = "W. F. Wong and E. Goto",
title = "Division and square-rooting using a split multiplier",
journal = j-ELECT-LETTERS,
volume = "28",
number = "18",
pages = "1758--1759",
day = "27",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A modification is proposed to the traditional design
of a fast floating point multiplication circuit such
that instead of just performing A$\times$B where A and
B are m bits long, it is also capable of \ldots{}",
}
@InProceedings{Woods:1992:HPD,
author = "R. F. Woods and S. E. McQuillan and J. Dowling and J.
V. McCanny",
booktitle = "Proceedings of Fifth Annual IEEE International ASIC
Conference and Exhibit, 1992",
title = "High performance {DSP} {ASIC} for multiply, divide and
square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "209--213",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The design of a high-speed ASIC that combines the
operations of multiplication, division and square root
is described. The chip is based on a systolic array
architecture that uses a redundant number system and
allows multiplication, division, and \ldots{}",
}
@Article{Yeyios:1992:TSA,
author = "A. K. Yeyios",
title = "On two sequences of algorithms for approximating
square roots",
journal = j-J-COMP-APPL-MATH,
volume = "40",
number = "1",
pages = "63--72",
month = jun,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Alzer:1993:SGF,
author = "Horst Alzer",
title = "Some gamma function inequalities",
journal = j-MATH-COMPUT,
volume = "60",
number = "201",
pages = "337--346",
month = jan,
year = "1993",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33B15 (26D20)",
MRnumber = "93f:33001",
MRreviewer = "Aurelio Cannizzo",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Periodical{Anonymous:1993:ITS,
author = "Anonymous",
title = "Integral transforms and special functions",
publisher = "Gordon and Breach Science Publishers",
address = "Yverdon, Switzerland",
year = "1993",
ISSN = "1065-2469, 1476-8291",
ISSN-L = "1065-2469",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Appears with variable frequency from 1993--2001, and
six times yearly from 2002--date.",
acknowledgement = ack-nhfb,
}
@Article{Bailey:1993:AMT,
author = "D. H. Bailey",
title = "Algorithm 719: Multiprecision Translation and
Execution of {FORTRAN} Programs",
journal = j-TOMS,
volume = "19",
number = "3",
pages = "288--319",
month = sep,
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Dec 13 18:37:31 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The author describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose. The second utility is a
translator program, which facilitates the conversion of
ordinary Fortran programs to use this package. By means
of source directives (special comments) in the original
Fortran program, the user declares the precision level
and specifies which variables in each subprogram are to
be treated as multiprecision. The translator program
reads this source program and outputs a program with
the appropriate multiprecision subroutine calls. This
translator supports multiprecision integer, real, and
complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6140D (High level languages); C6150C
(Compilers, interpreters and other processors); C7310
(Mathematics)",
keywords = "Algorithm 719; Arithmetic operations; Array space;
Complex data types; Computational expressions; Floating
point numbers; Fortran programs; Fortran subroutines;
Fortran utilities; Fortran-77 intrinsics; Mixed mode
operations; Multiprecision computation; Multiprecision
data types; Multiprecision subroutine calls;
Multiprecision translation; Operator precedence; Source
directives; Transcendental functions; Translator
program",
language = "English",
pubcountry = "USA",
thesaurus = "Data structures; Digital arithmetic; FORTRAN;
Mathematics computing; Program interpreters;
Subroutines",
}
@Article{Barrera:1993:IBS,
author = "Tony Barrera and Pelle Olsson",
title = "An Integer Based Square Root Algorithm",
journal = j-BIT,
volume = "33",
number = "2",
pages = "253--261",
month = jun,
year = "1993",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01989748;
http://dx.doi.org/10.1007/BF01989748",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68M07",
MRnumber = "1 326 017",
bibdate = "Wed Jan 4 18:52:23 MST 2006",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
abstract = "The authors propose a fast integer based method for
computing square roots of floating point numbers. This
implies high accuracy and robustness, since no
precision will be lost during the computation. Only
integer addition and shifts are necessary to obtain the
square root. Comparisons made with the modified Newton
method indicate that the suggested method is twice as
fast for computing floating point square roots. (5
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "AB Consonant, Uppsala, Sweden",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Floating point numbers; floating-point arithmetic;
Integer based square root algorithm; Modified Newton
method; Robustness",
pubcountry = "Denmark",
thesaurus = "Digital arithmetic",
xxpages = "254--261??",
}
@InCollection{Bohlender:1993:PAF,
author = "G. Bohlender and D. Cordes and A. Knofel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for accurate floating-point vector
arithmetic",
crossref = "Adams:1993:ACA",
pages = "87--102",
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Many computers provide accurate and reliable scalar
arithmetic for floating point numbers. An accurate
definition of the four elementary floating-point
operations +, -, *, / is given in the IEEE standards
for floating-point arithmetic and was well established
long before. An increasing number of computers
(especially PC's and workstations) feature IEEE
arithmetic. In many numerical algorithms, however,
compound operations such as the summation of a sequence
of numbers or the dot product of two vectors are highly
common. A simulation of these compound operations by
means of elementary floating-point operations leads to
accumulation of rounding errors and may suffer from
catastrophic cancellation of leading digits. Existing
standards for floating-point arithmetic do not improve
this situation. The goal of the proposal is to define
vector operations in a manner consistent with the
elementary scalar arithmetic operations. The rounding
modes and accuracy requirements as well as the data
formats of the operands and results of the vector
operations described in the proposal are chosen to be
fully consistent with the existing scalar
floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
bookpages = "x + 612",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
keywords = "Accuracy requirements; Catastrophic cancellation;
Compound operations; Data formats; Dot product;
Elementary floating-point operations; Elementary scalar
arithmetic operations; Floating point numbers; IEEE
arithmetic; IEEE standards; Leading digits; Numerical
algorithms; Operands; Rounding errors; Rounding modes;
Scalar floating-point arithmetic; Sequence; Standards;
Summation; Vector operations",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Mathematics computing; Roundoff
errors; Standards",
}
@Article{Cody:1993:ACP,
author = "W. J. Cody",
title = "Algorithm 714: {CELEFUNT}: {A} Portable Test Package
for Complex Elementary Functions",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "1--21",
month = mar,
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Sep 05 09:15:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
abstract = "This paper discusses CELEFUNT, a package of Fortran
programs for testing complex elementary functions.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
classification = "C4100 (Numerical analysis); C5230 (Digital
arithmetic methods); C7310 (Mathematics)",
keywords = "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
elementary functions; Complex power function;
CSIN/CCOS; CSQRT; Floating-point elementary functions;
Fortran programs; measurement; performance; Portable
test package",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
thesaurus = "Conformance testing; Digital arithmetic; FORTRAN;
Mathematics computing; Numerical analysis; Program
testing; Software packages",
}
@Article{duToit:1993:BFI,
author = "C. F. du Toit",
title = "{Bessel} functions {$J_n(z)$} and {$Y_n(z)$} of
integer order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "78",
number = "1--2",
pages = "181--189",
month = dec,
year = "1993",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(93)90153-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:41 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465593901534",
abstract = "This paper describes computer subroutines which were
developed to compute Bessel functions of the first and
second kind ($J_n(z)$ and $Y_n(z)$, respectively) for a
complex argument $z$ and a range of integer orders. A
novel way of determining the starting point of backward
recurrence is used, and the algorithm for $Y_n(z)$
improves on previous algorithms in terms of accuracy
and restrictions on the range of orders.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Book{Feinsilver:1993:ASO,
author = "Philip J. (Philip Joel) Feinsilver and Ren{\'e}
Schott",
title = "Algebraic structures and operator calculus",
volume = "241, 292, 347",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "?????",
year = "1993, 1994, 1996",
ISBN = "0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2),
0-7923-3834-0 (v. 3)",
ISBN-13 = "978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2),
978-0-7923-3834-5 (v. 3)",
LCCN = "QA432 .F45 1993",
bibdate = "Sat Oct 30 17:31:34 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Volume 1: Representations and probability theory.
Volume 2: Special functions and computer science.
Volume 3: Representations of Lie groups",
series = "Mathematics and its applications",
acknowledgement = ack-nhfb,
subject = "Calculus, Operational; Probabilities; Representations
of groups",
}
@Article{Fowkes:1993:HEA,
author = "R. E. Fowkes",
title = "Hardware Efficient Algorithms for Trigonometric
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "235--239",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.204796",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Frappier:1993:QFI,
author = "Cl{\'e}ment Frappier and Patrick Olivier",
title = "A quadrature formula involving zeros of {Bessel}
functions",
journal = j-MATH-COMPUT,
volume = "60",
number = "201",
pages = "303--316",
month = jan,
year = "1993",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "41A55 (65D32)",
MRnumber = "93d:41025",
MRreviewer = "Hans Strauss",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
C4130 (Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
Canada",
keywords = "Bessel functions; integration; interpolation; poles
and; polynomials; quadrature formula; sampling theorem;
zeros",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Han:1993:CAS,
author = "Weimin Han and Florian A. Potra",
title = "Convergence acceleration for some rootfinding
methods",
crossref = "Albrecht:1993:VNT",
volume = "9",
pages = "67--78",
year = "1993",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibdate = "Sun Oct 17 11:55:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Hu:1993:BRS,
author = "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
title = "On Bounding the Range of Some Elementary Functions in
{FORTRAN} 77",
journal = j-INTERVAL-COMP,
volume = "1993",
number = "3",
pages = "29--39",
year = "1993",
ISSN = "0135-4868",
MRclass = "65G10",
MRnumber = "1 305 844",
bibdate = "Wed Dec 4 11:13:33 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the International Conference on
Numerical Analysis with Automatic Result Verification
(Lafayette, LA, 1993)",
acknowledgement = ack-nhfb,
}
@TechReport{Karp:1993:HPD,
author = "A. H. Karp and P. Markstein",
title = "High precision division and square root",
number = "HPL-93-42",
institution = "Hewlett--Packard Lab.",
address = "Palo Alto, CA, USA",
pages = "20",
month = jun,
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present division and square root
algorithms for calculations with more bits than are
handled by the floating point hardware. These
algorithms avoid the need to multiply two high
precision numbers, speeding up the last iteration by as
much as a factor of ten.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Division; Floating point hardware; Square root
algorithms",
thesaurus = "Digital arithmetic",
}
@Article{Lee:1993:DAE,
author = "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
title = "Design of an area efficient unit for floating-point
division and square root",
journal = j-J-KOREA-INFO-SCI-SOCIETY,
volume = "20",
number = "7",
pages = "1060--1071",
month = jul,
year = "1993",
CODEN = "HJKHDC",
ISSN = "0258-9125",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors propose an algorithm for a high
performance floating point division and square root
unit that uses a parallel multiplier. The basic
algorithm used in the design is the continued-product
normalization method. In this method, an arbitrary
number is constantly multiplied to the divisor and
dividend and dividend/divisor ends up with quotient/1
and the desired result attained. However this method
requires computation of x*(2-x) and x*(3-x)/2 and this
is quite an overhead. Therefore they propose a new
algorithm to compute (2-x) and (3-x)/2 by using the
modified Booth algorithm. When applied to the
continued-product normalization method, this algorithm
can maximize the inherent parallelism of the
continued-product normalization method, and reduce
computation time by effectively applying pipelining,
and also achieve area efficient design by eliminating
one register and one carry propagate adder needed for
computing (2-x) and (3-x)/2. When the designed unit is
used with the seed generator which has the accuracy of
2/sup -7/, division can be executed in eight cycles and
the square root operation in 13 cycles.",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); C4240P (Parallel
programming and algorithm theory); C5120 (Logic and
switching circuits); C5230 (Digital arithmetic
methods)",
keywords = "Area efficient unit; Continued-product normalization
method; Floating-point division; Modified Booth
algorithm; Parallel multiplier; Pipelining; Seed
generator; Square root",
language = "Korean",
pubcountry = "South Korea",
thesaurus = "Adders; Digital arithmetic; Parallel algorithms",
}
@Article{Li:1993:CAF,
author = "Y. Li and X. Dong and S. Pan",
title = "Computation of Auxiliary Functions in {STO} Molecular
Integrals up to Arbitrary Accuracy. {I}. {Evaluation}
of Incomplete Gamma Function {E$_n$(X)} by Forward
Recursion",
journal = j-IJQC,
volume = "45",
number = "1",
pages = "3--??",
year = "1993",
CODEN = "IJQCB2",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
bibdate = "Wed Jan 3 14:24:13 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ijqc.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Litvinov:1993:ACR,
author = "Grigori L. Litvinov",
title = "Approximate construction of rational approximations
and the effect of error autocorrection",
type = "Technical report",
number = "8",
institution = "Institute of Mathematics, University of Oslo",
address = "Oslo, Norway",
month = may,
year = "1993",
bibdate = "Tue Mar 24 20:51:52 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Litvinov:1994:ACR}.",
acknowledgement = ack-nhfb,
}
@Article{Liu:1993:DSC,
author = "Hui Min Liu",
title = "Determination of several classes of elementary
functions by functional inequalities. (Chinese)",
journal = "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
volume = "11",
number = "2",
pages = "30--35, 12",
year = "1993",
ISSN = "1001-6074",
MRclass = "26A09 (39B72)",
MRnumber = "94g:26003",
MRreviewer = "Ling Yau Chan",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Louie:1993:DRS,
author = "M. E. Louie and M. D. Ercegovac",
booktitle = "Proceedings of the IEEE Workshop on FPGAs for Custom
Computing Machines, 5--7 April 1993",
title = "A digit-recurrence square root implementation for
field programmable gate arrays",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "178--183",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Creating efficient arithmetic processors requires a
pairing of high speed arithmetic algorithms with
optimal mapping strategies for a given technology. The
authors propose bit reduction as key to an efficient
pairing process for lookup table based \ldots{}",
}
@InProceedings{Lozier:1993:ABF,
author = "Daniel W. Lozier and F. W. J. Olver",
title = "{Airy} and {Bessel} Functions by Parallel Integration
of {ODEs}",
crossref = "Sincovec:1993:PSS",
pages = "530--538",
year = "1993",
bibdate = "Fri Jul 09 06:36:27 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Mathai:1993:HGS,
author = "A. M. Mathai",
title = "A handbook of generalized special functions for
statistical and physical sciences",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 235",
year = "1993",
ISBN = "0-19-853595-3",
ISBN-13 = "978-0-19-853595-9",
LCCN = "QA351 .M35 1993",
bibdate = "Sat Oct 30 18:57:40 MDT 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Oxford science publications",
URL = "http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html;
http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Handbooks, manuals, etc",
tableofcontents = "I Mathematical preliminaries \\
1.1 The gamma function 1 \\
1.2 Bernoulli polynomials 6 \\
1.3 Asymptotic expansions of gamma functions 9 \\
1.4 The psi function 11 \\
1.5 The generalized zeta functions 12 \\
1.6 The beta function 15 \\
1.7 Calculation of residues for gamma functions 16 \\
1.8 The Mellin transform 23 \\
1.9 Density functions 24 \\
1.10 Methods of deriving distributions 49 \\
2 The G-function \\
2.1 The G-function 60 \\
2.2 Some basic properties of the G-function 69 \\
2.3 The Mellin transform of a G-function 78 \\
2.4 Properties connected with the derivatives of a
G-function 94 \\
2.5 Series representations for a G-function 96 \\
2.6 G-functions as multiple integrals or as solutions
of integral equations 106 \\
2.7 Differential equation for a G-function 111 \\
2.8 Asymptotic expansions for a G-function 112 \\
3 Elementary special functions and the G-function \\
3.1 Gamma and related functions: notations and
definitions 117 \\
3.2 Hypergeometric functions: notations and special
cases 118 \\
3.3 Confluent hypergeometric function and related
functions 119 \\
3.4 Exponential integral and related functions 121 \\
3.5 Bessel functions and associated functions 121 \\
3.6 Other special functions 122 \\
3.7 Orthogonal polynomials 124 \\
3.8 Elementary special functions expressed in terms of
G-functions 127 \\
3.9 G-functions expressed in terms of elementary
special functions 129 \\
3.10 Some integrals involving G-functions 132 \\
3.11 The H-function 140 \\
3.12 Computational aspects of G- and H-functions 144
\\
3.13 Orders of the special functions for small and
large values of the argument 145 \\
4 Generalizations to matrix variables \\
4.1 Scalar functions of a symmetric positive definite
matrix 152 \\
4.2 Scalar functions of matrix arguments 158 \\
4.3 Laplace transform 160 \\
4.4 Hypergeometric functions of matrix arguments 171
\\
4.5 Generalized matrix transform or M-transform 177 \\
4.6 Zonal polynomial 194 \\
4.7 Matrix variate Dirichlet distribution 197 \\
4.8 Hypergeometric functions of many scalar variables
205 \\
4.9 Hypergeometric functions of many matrix arguments
215 \\
4.10 G- and H-functions of two variables 217 \\
Bibliography 227 \\
Glossary of symbols 231 \\
Author index 233 \\
Subject index 234",
}
@Article{Mazenc:1993:CFU,
author = "Christophe Mazenc and Xavier Merrheim and Jean-Michel
Muller",
title = "Computing functions $\cos^{-1}$ and $\sin^{-1}$ using
{Cordic}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "118--122",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.192222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@InProceedings{McQuillan:1993:NAV,
author = "S. E. McQuillan and J. V. McCanny and R. Hamill",
booktitle = "Proceedings of the 11th Symposium on Computer
Arithmetic, 2 July 1993",
title = "New algorithms and {VLSI} architectures for {SRT}
division and square root",
crossref = "Swartzlander:1993:SCA",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "80--86",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "Radix two algorithms for SRT division and
square-rooting are developed. For these schemes, the
result digits and the residuals are computed
concurrently and the computations in adjacent rows are
overlapped. Consequently, their performance should
\ldots{}",
}
@Article{Montuschi:1993:RIT,
author = "P. Montuschi and L. Ciminiera",
title = "Reducing iteration time when result digit is zero for
radix $2$ {SRT} division and square root with redundant
remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "239--246",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.204797",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Montuschi:1995:RRI}.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "A new architecture is presented for shared radix 2
division and square root whose main characteristic is
the ability to avoid any addition/subtraction, when the
digit 0 has been selected. The solution presented uses
a redundant representation of the \ldots{}",
}
@Article{Muller:1993:NAC,
author = "J{\"u}rgen M{\"u}ller",
title = "On numerical analytic continuation and convergence
acceleration by summability methods",
journal = "Analysis",
volume = "13",
number = "3",
pages = "279--291",
year = "1993",
ISSN = "0174-4747",
MRclass = "40G10 (40A30 41A25 65B10)",
MRnumber = "1245757 (94j:40013)",
MRreviewer = "S. Sridhar",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Analysis. International Mathematical Journal of
Analysis and its Applications",
keywords = "convergence acceleration",
}
@Article{Perger:1993:NEG,
author = "Warren F. Perger and Atul Bhalla and Mark Nardin",
title = "A numerical evaluator for the generalized
hypergeometric series",
journal = j-COMP-PHYS-COMM,
volume = "77",
number = "2",
pages = "249--254",
month = oct,
year = "1993",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(93)90008-Z",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 01 09:22:29 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
remark = "Uses extended precision complex arithmetic.",
}
@Book{Povolotskii:1993:OFR,
author = "A. I. Povolotski{\u{\i}} and G. A. Sviridyuk",
title = "{\cyr Odnomerny{\u{\i}}matematicheski{\u{\i}}analiz
{\`e}lementarnykh funktsi{\u{\i}}}. ({Russian})
[One-dimensional mathematical analysis of elementary
functions] {\cyr Nepreryvnye funktsii.
Differentsiruemye funktsii. Integriruemye funktsii}.
[Continuous functions. Differentiable functions.
Integrable functions]",
publisher = "Chelyabinsk. Gos. Univ.",
address = "Chelyabinsk, USSR",
pages = "92",
year = "1993",
ISBN = "5-230-17764-0",
ISBN-13 = "978-5-230-17764-7",
MRclass = "26-01 (00A05)",
MRnumber = "94e:26001",
MRreviewer = "J{\'o}zef Kalinowski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ratis:1993:CCH,
author = "Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba",
title = "A code to calculate (high order) {Bessel} functions
based on the continued fractions method",
journal = j-COMP-PHYS-COMM,
volume = "76",
number = "3",
pages = "381--388",
month = aug,
year = "1993",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(93)90062-H",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:39 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/001046559390062H",
abstract = "We have developed a fast code to calculate Bessel
functions of integer and fractional order based on the
continued fractions method. This algorithm is specially
useful in the case of Bessel functions of high order
because it does not require any recalculation using
normalization relations.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Book{Saurer:1993:BSF,
author = "Josef Saurer",
title = "Bases of special functions and their domains of
convergence",
volume = "73",
publisher = "Akademie Verlag GmbH",
address = "Berlin, Germany",
pages = "158",
year = "1993",
ISBN = "3-05-501613-0",
ISBN-13 = "978-3-05-501613-4",
ISSN = "0138-3019",
LCCN = "QA351 .S28 1993",
bibdate = "Sat Oct 30 18:53:24 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical research",
acknowledgement = ack-nhfb,
remark = "Revised version of the author's
thesis--Universit{\"a}t Essen, 1992.",
subject = "Functions, Special; Analytic functions; Eigenfunction
expansions; Convergence; Mathematical physics",
tableofcontents = "Introduction 9 \\
1 Foundations of the theory 15 \\
1.1 Holomorphic operator functions in Frechet spaces 15
\\
1.2 Floquet eigenvalue problems (with a regular
singular point) 22 \\
1.3 Relationships between differential operators
corresponding to Floquet eigenvalue problems for
systems of differential equations and scalar
differential equations 26 \\
1.4 Biholomorphic images of functions 30 \\
1.5 An expansion theorem 37 \\
2 First order differential systems with a regular
singular point 43 \\
2.1 Fundamental properties 44 \\
2.2 Construction of fundamental systems depending
holomorphically on parameters 46 \\
2.3 A family of second order differential equations 55
\\
2.4 Differential equations and special functions of
mathematical physics 57 \\
2.4.1 Bessel equation, Bessel function 57 \\
2.4.2 Whittaker equation, Whittaker function 58 \\
2.4.3 Hypergeometric equation, hypergeometric function
60 \\
2.4.4 Generalised spherical function 61 \\
3 Floquet eigenvalue problems for first order
differential systems with a regular singular point 63
\\
3.1 Construction of biorthogonal canonical systems of
eigen- and associated vectors of the operator functions
$T$ and $T^*$ 67 \\
3.2 A general expansion theorem 73 \\
3.3 Floquet eigenvalue problems and expansion theorems
for a family of second order differential equations 75
\\
4 Domains of convergence of the eigenfunction
expansions 83 \\
4.1 The Bessel and Whittaker case 85 \\
4.2 The hypergeometric case 95 \\
4.3 Typical domains of convergence 105 \\
5 Examples of expansions in series of special functions
109 \\
5.1 Expansions in series of Bessel functions 109 \\
5.2 Expansions in series of Whittaker functions 115 \\
5.3 Expansions in series of hypergeometric functions
119 \\
6 First order differential systems for products of
vector-valued functions 127 \\
6.1 Products of vectors and sums of matrices of
different dimensions 128 \\
6.2 Construction of the first order differential system
132 \\
7 Floquet eigenvalue problems and expansions in series,
of m - fold products of special functions 135 \\
7.1 Construction of biorthogonal canonical systems of
eigen- and associated vectors of the operator functions
$T$ and $T^*$ 142 \\
7.2 Application 145 \\
References 151 \\
Notation index 154 \\
Index 157",
}
@InProceedings{Schulte:1993:ERC,
author = "M. Schulte and E. Swartzlander",
title = "Exact rounding of certain elementary functions",
crossref = "Swartzlander:1993:SCA",
pages = "138--145",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
abstract = "An algorithm is described which produces exactly
rounded results for the functions of reciprocal, square
root, 2/sup x/, and log 2/sup x/. Hardware designs
based on this algorithm are presented for floating
point numbers with 16- and 24-b significands. These
designs use a polynomial approximation in which
coefficients are originally selected based on the
Chebyshev series approximation and are then adjusted to
ensure exactly rounded results for all inputs. To
reduce the number of terms in the approximation, the
input interval is divided into subintervals of equal
size and different coefficients are used for each
subinterval. For floating point numbers with 16-b
significands, the exactly rounded value of the function
can be computed in 51 ns on a 20-mm/sup 2/ chip. For
floating point numbers with 24-b significands, the
functions can be computed in 80 ns on a 98-mm/sup 2/
chip.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ.,
Austin, TX, USA",
bookpages = "xii + 284",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods)",
confdate = "29 June--2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "Elementary functions; Exact rounding; Floating point
numbers; Polynomial approximation; Reciprocal; Rounded
results; Square root",
thesaurus = "Floating point arithmetic; Function evaluation",
}
@Article{Schulte:1993:PHD,
author = "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
title = "Parallel hardware designs for correctly rounded
elementary functions",
journal = j-INTERVAL-COMP,
volume = "4",
pages = "65--88",
year = "1993",
ISSN = "0135-4868",
MRclass = "65G10 (65C20)",
MRnumber = "1 305 859",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the International Conference on
Numerical Analysis with Automatic Result Verification
(Lafayette, LA, 1993)",
acknowledgement = ack-nhfb,
}
@TechReport{Schwarz:1993:HRAa,
author = "E. Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Technical Report",
number = "CSL-TR-93-559",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jan,
year = "1993",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@PhdThesis{Schwarz:1993:HRAb,
author = "Eric Mark Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "224",
month = apr,
year = "1993",
bibdate = "Mon Jan 07 22:38:06 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Many common algorithms for high-order arithmetic
operations require an initial approximation. The
Newton--Raphson algorithm starts with an approximation
and then quadratically converges on the solution. The
initial approximation determines the number of
iterations of the algorithm and is typically
implemented as a look-up table in the form of a ROM or
PLA. A novel method is suggested which describes
high-order arithmetic operations with a partial product
array. This method applies to the operations of
division, reciprocal, square root, natural logarithm,
exponential, and trigonometric functions. The partial
product array of Boolean elements which describes the
operation can be summed on an existing floating-point
multiplier. The hardware needed is only the logic gates
to create the Boolean elements in the array and a
multiplexor, and the latency is that of the multiplier.
Thus, by reusing a floating-point multiplier, a
high-precision approximation to a high-order arithmetic
operation can be implemented with a low marginal
cost.\par
This dissertation describes the implementation and
shows a method for deriving partial product arrays to
approximate arithmetic operations. Then the proposed
method is applied and evaluated for several operations.
The proposed method yields a minimum approximation of
twelve bits correct for the reciprocal operation and
sixteen bits for the square root operation. The
proposed method is shown to be as small as 0.05\% the
size (in gates) of an equivalent precision look-up
table and has up to four times the accuracy (in bits)
as an equivalent latency polynomial approximation.
Also, three new iterative algorithms to increase the
precision of the approximations and a theoretical
analysis of the partial product array representation
are detailed. Thus, high-radix algorithms of many
arithmetic operations are possible at low cost.",
acknowledgement = ack-nhfb,
keywords = "division; elementary functions; exponential;
logarithm; PPA (partial product array); reciprocal
square root; square root",
remark = "AAT 9317816. ProQuest document ID 746798521.",
}
@InProceedings{Schwarz:1993:HSA,
author = "E. M. Schwarz and M. J. Flynn",
booktitle = "Proceedings of the 11th Symposium on Computer
Arithmetic, 2 July 1993",
title = "Hardware starting approximation for the square root
operation",
crossref = "Swartzlander:1993:SCA",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "103--111",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "A method for obtaining high-precision approximations
of high-order arithmetic operations is presented. These
approximations provide an accurate starting
approximation for high-precision iterative algorithms,
which translates into few iterations and \ldots{}",
}
@TechReport{Schwarz:1993:UFM,
author = "Eric Mark Schwarz and Flynn, M. J. (Michael J. )",
title = "Using a floating-point multiplier's internals for
high-radix division and square root",
type = "Technical report",
number = "CSL-TR-93-554",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "iv + 45",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.",
remark = "``January 1993.'' Abstract: ``A method for obtaining
high-precision approximations of high-order arithmetic
operations at low-cost is presented in this study.
Specifically, high-precision approximations of the
reciprocal (12 bits worst case) and square root (16
bits) operations are obtained using the internal
hardware of a floating-point multiplier without the use
of look-up tables. The additional combinatorial logic
necessary is very small due to the reuse of existing
hardware. These low-cost high-precision approximations
are used by iterative algorithms to perform the
operations of division and square root. The method
presented also applies to several other high-order
arithmetic operations. Thus, high-radix algorithms for
high-order arithmetic operations such as division and
square root are possible at low-cost.''",
}
@Article{Sellers:1993:CDC,
author = "H. Sellers",
title = "The {C$^2$-DIIS} Convergence Acceleration Algorithm",
journal = j-IJQC,
volume = "45",
number = "1",
pages = "31--??",
year = "1993",
CODEN = "IJQCB2",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
bibdate = "Wed Jan 3 14:24:13 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Shishkov:1993:RDB,
author = "Dimit{\cdprime}r Shishkov",
title = "Reduction of domains of basic elementary functions to
arbitrary small intervals",
journal = "Annuaire Univ. Sofia Fac. Math. Inform.",
volume = "87",
number = "1--2",
pages = "3--32 (1999)",
year = "1993",
ISSN = "0205-0808",
MRclass = "65D20",
MRnumber = "MR1745336",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment
Okhridski''. Fakultet po Matematika i Informatika.
Annuaire de l'Universit\'e de Sofia ``St. Kliment
Ohridski''. Facult\'e de Math\'ematiques et
Informatique",
}
@Article{Anonymous:1994:C,
author = "Anonymous",
title = "Corrigenda",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "553--553",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Mar 14 16:17:03 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hull:1994:ICE}",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
}
@Article{Bajard:1994:BNH,
author = "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel
Muller",
title = "{BKM}: a new hardware algorithm for complex elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "955--963",
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.295857",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07",
MRnumber = "1 294 301",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Bender:1994:DAS,
author = "Carl M. Bender and Stefan Boettcher",
title = "Determination of $f(\infty)$ from the asymptotic
series for $f(x)$ about $x = 0$",
journal = j-J-MATH-PHYS,
volume = "35",
number = "4",
pages = "1914--1921",
month = apr,
year = "1994",
CODEN = "JMAPAQ",
DOI = "http://dx.doi.org/10.1063/1.530577",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A60 (41A21 65D15 81Q15)",
MRnumber = "95d:41063",
bibdate = "Tue Nov 1 08:58:10 MDT 2011",
bibsource = "http://jmp.aip.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Brown:1994:CAS,
author = "Barry W. Brown and Lawrence Levy",
title = "Certification of {Algorithm 708}: Significant Digit
Computation of the Incomplete Beta",
journal = j-TOMS,
volume = "20",
number = "3",
pages = "393--397",
month = sep,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Nov 19 12:53:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{DiDonato:1992:ASD}.",
URL = "http://doi.acm.org/10.1145/192115.192155;
http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "algorithms; continued fractions; F-distribution",
subject = "G.1.2 [Numerical Analysis]: Approximation;",
}
@Article{Carlson:1994:AAS,
author = "B. C. Carlson and J. L. Gustafson",
title = "Asymptotic Approximations for Symmetric Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "25",
number = "2",
pages = "288--303",
month = mar,
year = "1994",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05 (41A60)",
MRnumber = "95b:33056",
MRreviewer = "Bruce C. Berndt",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/22847",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:1994:EDU,
author = "Sau-Gee Chen and Chieh-Chih Li",
booktitle = "{Proceedings of TENCON '94. IEEE Region 10's Ninth
Annual International Conference. Theme: `Frontiers of
Computer Technology'}",
title = "Efficient designs of unified $2$'s complement division
and square root algorithm and architecture",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "943--947",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Efficient unified 2's complement division and square
root algorithm, and their architectures are proposed in
this work. The designs are high speed, small area and
high compatibility. The architectures provide bit level
pipelined operation, as well \ldots{}",
}
@Article{Cortadella:1994:HRD,
author = "J. Cortadella and T. Lang",
title = "High-Radix Division and Square-Root with Speculation",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "919--931",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.295854",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-sfo # " and " # ack-nhfb,
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
summary = "The speed of high-radix digit-recurrence dividers and
square-root units is mainly determined by the
complexity of the result-digit selection. We present a
scheme in which a simpler function speculates the
result digit, and, when this speculation is \ldots{}",
}
@Article{Damnjanovic:1994:EFL,
author = "Zlatan Damnjanovic",
title = "Elementary functions and loop programs",
journal = j-NOTRE-DAME-J-FORM-LOG,
volume = "35",
number = "4",
pages = "496--522",
year = "1994",
CODEN = "NDJFAM",
ISSN = "0029-4527",
MRclass = "03D20 (68Q15)",
MRnumber = "96i:03036",
MRreviewer = "John P. Helm",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Das:1994:ATE,
author = "Mrinal Kanti Das",
title = "Analysis of two elementary functions",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "25",
number = "1",
pages = "17--24",
year = "1994",
CODEN = "IJMEBM",
ISSN = "0020-739X",
MRclass = "26-01 (33B10)",
MRnumber = "1 257 731",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Dunham:1994:PMAa,
author = "Charles B. Dunham",
title = "Provably Monotone Approximations, {IV}",
type = "Technical report",
number = "TR-417",
institution = "Department of Computer Science, University of Western
Ontario",
address = "London, Ontario, Canada",
day = "8",
month = mar,
year = "1994",
bibdate = "Tue Apr 12 11:26:47 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.csd.uwo.ca/tech-reports/",
acknowledgement = ack-nhfb,
}
@TechReport{Dunham:1994:PMAb,
author = "Charles B. Dunham",
title = "Provably Monotone Approximations, {IV}, Revised",
type = "Technical report",
number = "TR-422",
institution = "Department of Computer Science, University of Western
Ontario",
address = "London, Ontario, Canada",
day = "4",
month = apr,
year = "1994",
bibdate = "Tue Apr 12 11:26:47 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.csd.uwo.ca/tech-reports/",
acknowledgement = ack-nhfb,
}
@Article{Dunkl:1994:AHI,
author = "Charles F. Dunkl and Donald E. Ramirez",
title = "{Algorithm 736}: Hyperelliptic Integrals and the
Surface Measure of Ellipsoids",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "427--435",
month = dec,
year = "1994",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/198429.198431",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D30",
MRnumber = "1 368 025",
bibdate = "Tue Mar 14 16:16:51 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "elliptic integral; expected radius; Lauricella's
hypergeometric function; optimal designs; surface
measure",
subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical
Differentiation -- multiple quadrature; G.3
[Mathematics of Computing]: Probability and
Statistics",
}
@Article{Dunkl:1994:CHI,
author = "Charles F. Dunkl and Donald E. Ramirez",
title = "Computing Hyperelliptic Integrals for Surface Measure
of Ellipsoids",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "413--426",
month = dec,
year = "1994",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/198429.198430",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D30",
MRnumber = "1 368 024",
bibdate = "Tue Mar 14 16:16:49 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "elliptic integral; expected radius; Lauricella's
hypergeometric function; optimal designs; surface
measure",
subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical
Differentiation -- multiple quadrature; G.3
[Mathematics of Computing]: Probability and
Statistics",
}
@Book{Ercegovac:1994:DSR,
author = "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
title = "Division and square root: digit-recurrence algorithms
and implementations",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "x + 230",
year = "1994",
ISBN = "0-7923-9438-0",
ISBN-13 = "978-0-7923-9438-9",
LCCN = "QA76.9.C62 E73 1994",
bibdate = "Fri Mar 27 09:46:24 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fukushima:1994:NCI,
author = "Toshio Fukushima and Hideharu Ishizaki",
title = "Numerical computation of incomplete elliptic integrals
of a general form",
journal = j-CELEST-MECH-DYN-ASTR,
volume = "59",
number = "3",
pages = "237--251",
month = jul,
year = "1994",
CODEN = "CLMCAV",
DOI = "http://dx.doi.org/10.1007/BF00692874",
ISSN = "0923-2958 (print), 1572-9478 (electronic)",
ISSN-L = "0923-2958",
MRclass = "33E05 65R20 65D32 (33E30 70-08 70E15)",
MRnumber = "1285916 (95c:65041)",
bibdate = "Wed Oct 20 21:26:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/0923-2958/",
abstract = "We present an algorithm to compute the incomplete
elliptic integral of a general form. The algorithm
efficiently evaluates some linear combinations of
incomplete elliptic integrals of all kinds to a high
precision. Some numerical examples are given as
illustrations. This enables us to numerically calculate
the values and the partial derivatives of incomplete
elliptic integrals of all kinds, which are essential
when dealing with many problems in celestial mechanics,
including the analytic solution of the torque-free
rotational motion of a rigid body around its
barycenter.",
acknowledgement = ack-nhfb,
fjournal = "Celestial Mechanics \& Dynamical Astronomy. An
International Journal of Space Dynamics",
keywords = "Incomplete elliptic integrals; numerical computation",
ZMnumber = "Zbl 0818.33013",
}
@Article{Hahn:1994:UDF,
author = "H. Hahn and D. Timmermann and B. J. Hosticka and B.
Rix",
title = "A unified and division-free {CORDIC} argument
reduction method with unlimited convergence domain
including inverse hyperbolic functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "11",
pages = "1339--1344",
month = nov,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.324568",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:58 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@InProceedings{Homeier:1994:NCA,
author = "Herbert H. H. Homeier",
editor = "Ralf Gruber and Marco Tomassini",
booktitle = "Proceedings of the 6th {Joint EPS-APS International
Conference} on {Physics Computing, Physics Computing}
'94",
title = "Nonlinear convergence acceleration for orthogonal
series",
publisher = "European Physical Society, Boite Postale 69, CH-1213
Petit-Lancy, Geneva, Switzerland",
address = "Lugano",
pages = "47--50",
year = "1994",
ISBN = "2-88270-011-3",
ISBN-13 = "978-2-88270-011-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942",
keywords = "convergence acceleration",
tech = "Technical Report TC-NA-94-2, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1994",
}
@Article{Hull:1994:ICE,
author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
Tang",
title = "Implementing Complex Elementary Functions Using
Exception Handling",
journal = j-TOMS,
volume = "20",
number = "2",
pages = "215--244",
month = jun,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Mar 21 15:10:29 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Anonymous:1994:C}.",
abstract = "Algorithms are developed for reliable and accurate
evaluations of the complex elementary functions
required in Fortran 77 and Fortran 90, namely cabs,
csqrt, cexp, clog, csin, and ccos. The algorithms are
presented in a pseudocode that has a convenient
exception-handling facility. A tight error bound is
derived for each algorithm. Corresponding Fortran
programs for an IEEE environment have also been
developed to illustrate the practicality of the
algorithms, and these programs have been tested very
carefully to help confirm the correctness of the
algorithms and their error bounds. The results are of
these tests are included in the paper, but the Fortran
programs are not; the programs are available from
Fairgrieve, (tff@cs.toronto.edu).",
acknowledgement = ack-nhfb,
keywords = "algorithms; complex elementary functions; design;
implementation",
subject = "G.1.0 [Numerical Analysis]: General--error analysis;
numerical algorithms; G.1.2 [Numerical Analysis]:
Approximation--elementary function approximation; G.4
[Mathematics of Computing]: Mathematical
Software--algorithm analysis; reliability and
robustness; verification",
}
@Article{Iserles:1994:CAD,
author = "A. Iserles",
title = "Convergence acceleration as a dynamical system",
journal = j-APPL-NUM-MATH,
volume = "15",
number = "2",
pages = "101--121",
day = "13",
month = sep,
year = "1994",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "58F23 (30D05 58F08 65D99 65H99)",
MRnumber = "95i:58155",
MRreviewer = "Peter M. Makienko",
bibdate = "Wed Jul 28 14:35:48 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Innovative methods in numerical analysis (Bressanone,
1992).",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Jablonski:1994:NES,
author = "Aleksander Jablonski",
title = "Numerical Evaluation of Spherical {Bessel} Functions
of the First Kind",
journal = j-J-COMPUT-PHYS,
volume = "111",
number = "2",
pages = "256--259",
month = apr,
year = "1994",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1006/jcph.1994.1060",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:54:54 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999184710606",
abstract = "Calculations of cross sections for elastic scattering
of electrons require frequent evaluations of the
spherical Bessel functions, $jl(x)$ and $nl(x)$, in a
wide range of the argument $x$ and the order $l$. It
turns out that the usual algorithms providing the
values of the spherical Bessel function of the first
kind, $jl(x)$, have a rather limited range of
stability. It is shown that there is no algorithm
implementing a single method which can be used in
calculations associated with the theory of elastic
scattering of electrons. An attempt is made to select
different areas of stability from different algorithms
in order to create a relatively fast and universal
algorithm.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@InProceedings{Jain:1994:SRR,
author = "V. K. Jain and Lei Lin",
booktitle = "IEEE International Conference on Acoustics, Speech,
and Signal Processing: ICASSP-94, 19--22 April 1994",
title = "Square-root, reciprocal, sine\slash cosine, arctangent
cell for signal and image processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II/521--II/524",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper discusses an efficient interpolation method
for nonlinear function generation. Based on this, a 24
bit VLSI cell, capable of computing the (1) square
root, (2) reciprocal, (3) sine/cosine, and (4)
arctangent functions, is presented for \ldots{}",
}
@Article{Kearfott:1994:AIP,
author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
title = "Algorithm 737: {INTLIB}: {A} Portable {Fortran}-77
Elementary Function Library",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "447--459",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat May 20 15:54:18 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
accepted = "December 1993",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic;
operator overloading; standard functions",
subject = "D.2.2 [Software Engineering]: Tools and Techniques --
software libraries; D.2.7 [Software Engineering]:
Distribution and Maintenance -- documentation;
portability; G.1.0 [Numerical Analysis]: General --
computer arithmetic; G.1.2 [Numerical Analysis]:
Approximation -- elementary function approximation",
}
@Article{Khajah:1994:UHP,
author = "H. G. Khajah and E. L. Ortiz",
title = "Ultra-high precision computations",
journal = j-COMP-MATH-APPL,
volume = "27",
number = "7",
pages = "41--57",
month = apr,
year = "1994",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(94)90148-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Mon Jun 13 22:03:39 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122194901481",
abstract = "We describe a machine independent Fortran subroutine
which performs the four basic arithmetic operations
with a degree of accuracy prescribed by the user.
Tables of Chebyshev expansions of orders 48 and 50 for
some basic mathematical functions are obtained as a
result of applying this subroutine in conjunction with
the recursive formulation of the Tau Method. A recently
devised technique for the sharp determination of upper
and lower error bounds for Tau Method approximations
enables us to find the degree $n$ required to achieve a
prescribed accuracy $\epsilon$ over a given interval
$[a, b]$. A number of practical illustrations are
given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Imperial Coll. of Sci., Technol. and
Med., London, UK",
classification = "C6140D (High level languages); C7310 (Mathematics)",
keywords = "$\cos(\pi x)$; $\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$;
$\sin(\pi x)$; $x \exp(x^2) erfc(x)$; $z \exp(z)
\Ei(-z)$; Arithmetic operations; Chebyshev expansions;
Lower error bounds; Machine independent Fortran
subroutine; Mathematical functions; Tau method; Upper
error bounds",
pubcountry = "UK",
thesaurus = "FORTRAN; Mathematics computing",
}
@Article{Lewanowicz:1994:SAS,
author = "Stanis{\l}aw Lewanowicz",
title = "A simple approach to the summation of certain slowly
convergent series",
journal = j-MATH-COMPUT,
volume = "63",
number = "208",
pages = "741--745",
month = oct,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65B10",
MRnumber = "95a:65010",
MRreviewer = "Thomas A. Atchison",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
}
@Article{Litvinov:1994:ACR,
author = "Grigori L. Litvinov",
title = "Approximate construction of rational approximations
and the effect of error autocorrection",
journal = j-RUSS-J-MATH-PHYS,
volume = "1",
number = "3",
pages = "313--352",
month = "????",
year = "1994",
CODEN = "RJMPEL",
ISSN = "1061-9208",
bibdate = "Tue Mar 24 20:54:11 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arxiv.org/abs/math/0101042",
abstract = "Several construction methods for rational
approximations to functions of one real variable are
described in the present paper; the computational
results that characterize the comparative accuracy of
these methods are presented; an effect of error
autocorrection is considered. This effect occurs in
efficient methods of rational approximation (e.g.,
Pad{\'e} approximations, linear and nonlinear Pad{\'e}
Chebyshev approximations) where very significant errors
in the coefficients do not affect the accuracy of the
approximation. The matter of import is that the errors
in the numerator and the denominator of a fractional
rational approximant compensate each other. This effect
is related to the fact that the errors in the
coefficients of a rational approximant are not
distributed in an arbitrary way but form the
coefficients of a new approximant to the approximated
function. Understanding of the error autocorrection
mechanism allows to decrease this error by varying the
approximation procedure depending on the form of the
approximant. Some applications are described in the
paper. In particular, a method of implementation of
basic calculations on decimal computers that uses the
technique of rational approximations is described in
the Appendix.\par
To a considerable extent the paper is a survey and the
exposition is as elementary as possible.",
acknowledgement = ack-nhfb,
}
@InCollection{Lozier:1994:NES,
author = "Daniel W. Lozier and F. W. J. Olver",
title = "Numerical evaluation of special functions",
crossref = "Gautschi:1994:MCH",
volume = "48",
pages = "79--125",
year = "1994",
MRclass = "65D20 (30-04 33-04 41-04)",
MRnumber = "95m:65036",
MRreviewer = "John P. Coleman",
bibdate = "Fri Jul 9 05:44:10 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Proc. Sympos. Appl. Math.",
URL = "http://math.nist.gov/mcsd/Reports/2001/nesf/",
abstract = "Higher transcendental functions continue to play
varied and important roles in investigations by
engineers, mathematicians, scientists, and
statisticians. The purpose of this paper is to assist
in locating useful approximations and software for the
numerical generation of these functions, and to offer
some suggestions for future developments in the
field.",
acknowledgement = ack-nhfb,
remark = "The references list contains about 400 entries which
should ultimately be incorporated in this BibTeX
bibliography collection.",
}
@TechReport{Lozier:1994:SNS,
author = "Daniel W. Lozier",
title = "Software Needs in Special Functions",
type = "Technical Report",
number = "NISTIR 5490",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "16",
month = aug,
year = "1994",
bibdate = "Fri Jul 09 05:47:26 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Lozier:1996:SNS}.",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
acknowledgement = ack-nhfb,
}
@InProceedings{Magnus:1994:ASA,
author = "Alphonse P. Magnus",
title = "Asymptotics and super asymptotics of best rational
approximation error norms for the exponential function
(the `$1/9$' problem) by the
{Carath{\'e}odory--Fej{\'e}r} method",
crossref = "Cuyt:1994:NNM",
pages = "173--185",
year = "1994",
bibdate = "Mon Nov 24 21:30:41 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ZMnumber = "809.41015",
}
@Article{Marsaglia:1994:REI,
author = "George Marsaglia and Arif Zaman and John C. W.
Marsaglia",
title = "Rapid evaluation of the inverse of the normal
distribution function",
journal = j-STAT-PROB-LETT,
volume = "19",
number = "4",
pages = "259--266",
day = "15",
month = mar,
year = "1994",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/0167-7152(94)90174-0",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "65U05",
MRnumber = "1 278 658",
bibdate = "Thu Dec 22 07:42:24 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
abstract = "This is an interesting article with direct application
in generating normal random variable by computer
programs. The suggested applications are related to
Monte Carlo simulation based on massively parallel
systems or supercomputers. The idea is to replace
larger programs with complicated computations and with
difficulties in accuracy controlling by simpler
arithmetic programs that use tabled constants. These
seem to be the normal evolution since memory becomes
cheaper and cheaper.\par
The authors compute the inverse of the cPhi function
$$cPhi(x) = (2/\pi)^{1/2} \int^\infty_x \exp (-t^2/2)
dt=u,$$ using a uniform random variable as input and
the truncated Taylor series development of it. In order
to increase the speed the coefficients of the truncated
Taylor series $$x(u_0+h) = x(u_0) + x'(u_0) \cdot h +
{1 \over 2} x''(u_0) \cdot h^2 + {1 \over 6} x'''(u_0)
\cdot h^3,$$ are predetermined for 1024 points. And
here comes another bright idea: the 1024 points are
chosen based on the representation of the uniform
random variable in modern computers as floating point
variable of the form: $u=2^{-k} ((1/2) + (j/64)) +
2^{-k} \cdot (m/2^{24})$ with $0 \le k<32$, $0 \le
j<32$ and $0 \le m<2^{18}$ and considering 32 bit
representation.\par
With this assumptions and the truncation to the third
power of $h$ of the Taylor series, the authors show
that the error does not exceed the limit of single
precision accuracy. Furthermore the calculations are
speeded up based on reducing multiplications. A number
of FORTRAN programs are also presented in order to
evaluate the complementary normal distribution function
cPhi (several versions) with great accuracy, create the
constant tables, and generate the normal distribution
variable. These simple programs give the user the
possibility to completely control the accuracy.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
keywords = "cPhi function; FORTRAN programs; massive parallel
systems; Monte Carlo simulation; normal distribution
function; normal random variable; supercomputers;
truncated Taylor series",
ZMclass = "*65C99 Numerical simulation 65C05 Monte Carlo methods
60-04 Machine computation, programs (probability
theory) 60E05 General theory of probability
distributions 62E17 Approximations to statistical
distributions (nonasymptotic)",
ZMnumber = "0798.65132",
ZMreviewer = "A. Pasculescu (Bucuresti)",
}
@Article{Merrheim:1994:CEF,
author = "X. Merrheim",
title = "The computation of elementary functions in radix
$2^p$",
journal = j-COMPUTING,
volume = "53",
number = "3--4",
pages = "219--232",
year = "1994",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68M07",
MRnumber = "95j:68028",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics (Vienna,
1993).",
acknowledgement = ack-nhfb,
}
@Article{Narayanaswami:1994:AE,
author = "Chandrasekhar Narayanaswami and William Luken",
title = "Approximating $x^n$ efficiently",
journal = j-INFO-PROC-LETT,
volume = "50",
number = "4",
pages = "205--210",
day = "25",
month = may,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
MRclass = "65D20 (41-04 65B99)",
MRnumber = "95b:65031",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM Advanced Workstations and Systems Div",
affiliationaddress = "Austin, TX, USA",
classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
(Interpolation and function approximation); C4130
(Interpolation and function approximation); C6130B
(Graphics techniques)",
corpsource = "IBM Adv. Workstations and Syst. Div., Austin, TX,
USA",
journalabr = "Inf Process Lett",
keywords = "$x^n$ approximation; approximation theory;
Approximation theory; Color computer graphics;
Computational complexity; Computational methods;
computer graphics; elementary functions; floating-point
arithmetic; Function evaluation; graphics modeling;
Image quality; Light intensity computation; look-up
tables; performance requirements; Polynomial
evaluation; Polynomials; polynomials; power function;
scientific applications; Semiconducting silicon; Table
lookup",
treatment = "T Theoretical or Mathematical",
}
@Article{Nishioka:1994:EFB,
author = "Keiji Nishioka",
title = "Elementary functions based on elliptic curves",
journal = j-TOKYO-J-MATH,
volume = "17",
number = "2",
pages = "439--446",
year = "1994",
ISSN = "0387-3870",
MRclass = "12H05",
MRnumber = "96b:12011",
MRreviewer = "Alexandru Buium",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ohta:1994:INP,
author = "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and
Nobuaki Yoshida",
title = "Improvement and new proposal on fast evaluation of
elementary functions. (Japanese)",
journal = j-TRANS-INFO-PROCESSING-SOC-JAPAN,
volume = "35",
number = "5",
pages = "926--933",
month = may,
year = "1994",
CODEN = "JSGRD5",
ISSN = "0387-5806",
MRclass = "65D20",
MRnumber = "95f:65045",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
1570-1579, 1993) introduced fast methods for numerical
evaluation of elementary functions based on table
lookup. They are called ATA (add/table-lookup/add) and
ATA-M (add/table-lookup/add and multiply) methods for
single- and double-precision calculations respectively.
In this paper, an improvement to these methods that
shrinks the size of the table by a factor of about 3/16
is presented. Another method called the `split parallel
multiplication method', which is characterized by
simpler table lookup than ATA-M and by split and
parallel use of double-precision floating point
circuitry, is also introduced, These new methods fit on
to integrated circuits of a size comparable with
commercially available floating-point accelerators.
Methods for accelerating double-precision division,
generating uniform pseudo-random numbers in
double-precision, and accelerating the multiplication
of single-precision complex numbers using the same
circuitry are proposed.",
acknowledgement = ack-nhfb,
affiliation = "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods); C6130 (Data handling techniques)",
keywords = "Add/table-lookup/add method;
Add/table-lookup/add/multiply method; ATA method; ATA-M
method; Double-precision calculations; Double-precision
division; Double-precision floating point circuitry;
Elementary functions evaluation; Floating-point
accelerators; Integrated circuits; Numerical
evaluation; Single-precision calculations;
Single-precision complex number multiplication; Split
parallel multiplication method; Table size; Uniform
pseudo-random number generation",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Digital arithmetic; Function evaluation; Random number
generation; Table lookup",
}
@Article{Osada:1994:CAM,
author = "Naoki Osada",
title = "Convergence acceleration methods",
journal = "S\=urikaisekikenky\=usho K\=oky\=uroku",
volume = "880",
number = "??",
pages = "28--43",
month = "????",
year = "1994",
MRclass = "65B05",
MRnumber = "1366233",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "The state of the art of scientific computing and its
prospects (Japanese) (Kyoto, 1993)",
acknowledgement = ack-nhfb,
fjournal = "S\=urikaisekikenky\=usho K\=oky\=uroku",
keywords = "convergence acceleration",
}
@InProceedings{Rappoport:1994:TMC,
author = "Juri M. Rappoport",
title = "The {Tau-Method} and the Computation of the {Bessel}
Functions of the Complex Order",
crossref = "Brown:1994:PCL",
pages = "353--355",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Schulte:1994:HDE,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Hardware Design for Exactly Rounded Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "964--973",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.295858",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This paper presents hardware designs that produce
exactly rounded results for the functions of
reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
These designs use polynomial approximation in which the
terms in the approximation are generated in parallel,
and then summed by using a multi-operand adder. To
reduce the number of terms in the approximation, the
input interval is partitioned into subintervals of
equal size, and different coefficients are used for
each subinterval. The coefficients used in the
approximation are initially determined based on the
Chebyshev series approximation. They are then adjusted
to obtain exactly rounded results for all inputs.
Hardware designs are presented, and delay and area
comparisons are made based on the degree of the
approximating polynomial and the accuracy of the final
result. For single-precision floating point numbers, a
design that produces exactly rounded results for all
four functions has an estimated delay of 80 ns and a
total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
technology. Allowing the results to have a maximum
error of one unit in the last place reduces the
computational delay by 5\% to 30\% and the area
requirements by 33\% to 77\%.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ.,
Austin, TX, USA",
classification = "B0290F (Interpolation and function approximation);
B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5120 (Logic and switching circuits);
C5230 (Digital arithmetic methods)",
keywords = "1 Micron; 1.0-Micron CMOS technology; Argument
reduction; Chebyshev series approximation; Chip area;
Computational delay; Computer arithmetic; Exact
rounding; Exactly rounded elementary functions;
Hardware designs; Multi-operand adder; Parallel
multiplier; Polynomial approximation; Reciprocal;
Single-precision floating point numbers;
Special-purpose hardware; Square-root",
language = "English",
numericalindex = "Size 1.0E-06 m",
pubcountry = "USA",
thesaurus = "Approximation theory; Chebyshev approximation; CMOS
integrated circuits; Digital arithmetic; Multiplying
circuits; Polynomials; Summing circuits",
}
@Article{Spouge:1994:CGD,
author = "John L. Spouge",
title = "Computation of the Gamma, Digamma, and Trigamma
Functions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "31",
number = "3",
pages = "931--944",
month = jun,
year = "1994",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "33B15 (30E10 33-04 40-04 65D20)",
MRnumber = "95g:33002",
MRreviewer = "E. Kaucher",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Timmermann:1994:CFV,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} floating-point vector-arithmetic unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "29",
number = "5",
pages = "634--639",
month = may,
year = "1994",
CODEN = "IJSCBC",
DOI = "http://dx.doi.org/10.1109/4.284719",
ISSN = "0018-9200",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This work describes a floating-point arithmetic unit
based on the CORDIC algorithm. The unit computes a full
set of high level arithmetic and elementary functions:
multiplication, division, (co)sine, hyperbolic
(co)sine, square root, natural logarithm, inverse
(hyperbolic) tangent, vector norm, and phase. The chip
has been integrated in 1.6 mu m double-metal n-well
CMOS technology and achieves a normalized peak
performance of 220 MFLOPS.",
acknowledgement = ack-nhfb,
affiliation = "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
Duisburg, Germany",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5120 (Logic and switching circuits); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods)",
keywords = "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
Division; Double-metal n-well CMOS technology;
Floating-point vector-arithmetic unit; Hyperbolic sine;
Inverse tangent; Multiplication; Natural logarithm;
Phase; Sine; Square root; Vector norm",
language = "English",
numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
pubcountry = "USA",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Integrated logic circuits; Parallel architectures;
Pipeline processing; Vector processor systems",
}
@Article{Turner:1994:SRM,
author = "Stephen M. Turner",
title = "Square roots mod $p$",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "5",
pages = "443--449",
month = may,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A07",
MRnumber = "95c:11004",
MRreviewer = "David Lee Hilliker",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Watanabe:1994:MSP,
author = "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu
Oguni",
title = "Mathematical Software for the {P.C.} and Work
Stations: {A} Collection of {Fortran 77} Programs",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xiv + 387",
month = jun,
year = "1994",
ISBN = "0-444-82000-0",
ISBN-13 = "978-0-444-82000-6",
LCCN = "QA 76.73 F25 F6813 1994",
bibdate = "Sun Sep 28 10:42:07 MDT 1997",
bibsource = "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/;
http://www.cbooks.com/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translation of: FORTRAN 77 ni yoru suchi keisan
sofutowea.",
price = "US\$178.50",
URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000",
acknowledgement = ack-nhfb,
alttitle = "{Fortran 77} ni yoru suchi keisan sofutowea.
English.",
keywords = "Fortran 77 (computer program language); Numerical
analysis --- Use of --- Computers; {Fortran 77}
(Computer program language)",
}
@InProceedings{Wong:1994:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in double
precision",
crossref = "Mudge:1994:PTS",
pages = "349--358",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "One of the most spectacular development in computer
technology is the growth in memory density and speed.
It is with this development in mind that we intend to
tackle the old problem of computing the elementary
functions. Since the dawn of computing, the fast and
accurate computation of the elementary functions has
been a constant concern of numerical computing. It now
seems possible to use tables of sizes in the range of
megabits to aid in such computation. To this end, in
this paper, we propose a method called ATA-M (Add-Table
Lookup-Add with Multiplication) for evaluating
polynomials with the aid of tables. When applied to the
elementary functions, we obtained a set of algorithms
which computes the reciprocal, square root,
exponential, sine, cosine, logarithm, are tangent and
the hyperbolic functions in about 3 to 4 double
precision floating point multiplication time and
utilizing about 2 Mbyte of tables.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
bookpages = "xi + 621",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
confdate = "4-7 Jan. 1994",
conflocation = "Wailea, HI, USA",
confsponsor = "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
Admin",
keywords = "Add-Table Lookup-Add with Multiplication; ATA-M;
Double precision; Elementary functions; Floating point
multiplication time; Hyperbolic functions; Memory
density; Memory speed; Numerical computing;
Polynomials",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Polynomials; Table lookup",
}
@Article{Wong:1994:FHB,
author = "W. F. Wong and E. Goto",
title = "Fast Hardware-Based Algorithms for Elementary Function
Computations Using Rectangular Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "3",
pages = "278--294",
month = mar,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.272429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:54 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
abstract = "As the name suggests, elementary functions play a
vital role in scientific computations. Yet due to their
inherent nature, they are a considerable computing task
by themselves. Not surprisingly, since the dawn of
computing, the goal of speeding up elementary function
computation has been pursued. This paper describes new
hardware based algorithms for the computation of the
common elementary functions, namely division,
logarithm, reciprocal square root, arc tangent, sine
and cosine. These algorithms exploit microscopic
parallelism using specialized hardware with heavy use
of truncation based on detailed accuracy analysis. The
contribution of this work lies in the fact that these
algorithms are very fast and yet are accurate. If we
let the time to perform an IEEE Standard 754 double
precision floating point multiplication be
$\tau_\times$, our algorithms to achieve roughly $3.68
\tau_\times$, $4.56 \tau_\times$, $5.25 \tau_\times$,
$3.69 \tau_\times$, $7.06 \tau_\times$, and $6.5
\tau_\times$, for division, logarithm, square root,
exponential, are tangent and complex exponential (sine
and cosine) respectively. The trade-off is the need for
tables and some specialized hardware. The total amount
of tables required, however, is less than 128 Kbytes.
We discuss the hardware, algorithmic and accuracy
aspects of these algorithms.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "IEEE Transactions on Computers",
keywords = "Arc tangent; Common elementary functions; Cosine;
Elementary function computations; Floating point
multiplication; Hardware-based algorithms; Microscopic
parallelism; Reciprocal square root; Rectangular
multipliers; Scientific computations; Sine",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Error analysis",
}
@Article{Xu:1994:VPC,
author = "Guo Liang Xu and Jia Kai Li",
title = "Variable precision computation of elementary
functions. (Chinese)",
journal = j-J-NUMER-METHODS-COMPUT-APPL,
volume = "15",
number = "3",
pages = "161--171",
year = "1994",
ISSN = "1000-3266",
MRclass = "65D20 (65Y20)",
MRnumber = "MR1357336 (96i:65013)",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal on Numerical Methods and Computer
Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}
@Article{Abad:1995:CRC,
author = "Julio Abad and Javier Sesma",
title = "Computation of the Regular Confluent Hypergeometric
Function",
journal = j-MATHEMATICA-J,
volume = "5",
number = "4",
pages = "??--??",
month = "Fall",
year = "1995",
CODEN = "????",
ISSN = "1047-5974",
bibdate = "Sat Nov 6 13:34:06 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.mathematica-journal.com/issue/v5i4/",
URL = "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
acknowledgement = ack-nhfb,
}
@Article{Amos:1995:RAP,
author = "D. E. Amos",
title = "A Remark on {Algorithm 644}: {A} Portable Package for
{Bessel} Functions of a Complex Argument and
Nonnegative Order",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "388--393",
month = dec,
year = "1995",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/212066.212078",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Mar 09 10:24:54 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See
\cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
acknowledgement = ack-rfb,
keywords = "complex Airy Functions; complex Bessel functions;
derivatives of Airy functions; H, I, J, K, and Y Bessel
functions; log gamma function",
subject = "G.1.0 [Numerical Analysis]: General -- numerical
algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
G.m [Mathematics of Computing]: Miscellaneous",
}
@Article{Baratchart:1995:RIE,
author = "L. Baratchart and E. B. Saff and F. Wielonsky",
title = "Rational interpolation of the exponential function",
journal = j-CAN-J-MATH,
volume = "47",
number = "??",
pages = "1121--1147",
month = "????",
year = "1995",
CODEN = "CJMAAB",
DOI = "http://dx.doi.org/10.4153/CJM-1995-058-6",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:39:05 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v47/;
http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
}
@Article{Carlson:1995:NCR,
author = "B. C. Carlson",
title = "Numerical computation of real or complex elliptic
integrals",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "1--2",
pages = "13--26",
month = jul,
year = "1995",
CODEN = "NUALEG",
DOI = "http://dx.doi.org/10.1007/BF02198293",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
MRclass = "33Exx (33-04 65D20)",
MRnumber = "1 345 407",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Special functions (Torino, 1993)",
abstract = "Algorithms for numerical computation of symmetric
elliptic integrals of all three kinds are improved in
several ways and extended to complex values of the
variables (with some restrictions in the case of the
integral of the third kind). Numerical check values,
consistency checks, and relations to Legendre's
integrals and Bulirsch's integrals are included.",
acknowledgement = ack-nhfb,
classification = "B0290R (Integral equations); C4180 (Integral
equations)",
conflocation = "Torino, Italy; 14-15 Oct. 1993",
conftitle = "International Joint Symposium on Special Functions and
Artificial Intelligence",
corpsource = "Ames Lab., Iowa State Univ., Ames, IA, USA",
keywords = "Bulirsch's integrals; complex elliptic integrals;
complex values; consistency checks; elliptic equations;
integral equations; Legendre's integrals; numerical
analysis; numerical check values; numerical computation
algorithms; real elliptic integrals",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Chen:1995:UCA,
author = "San-Gee Chen and Chieh-Chih Li",
booktitle = "IEEE Signal Processing Society Workshop on VLSI Signal
Processing, VIII, 1995",
title = "A unified cellular array for multiplication, division
and square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "533--541",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A unified fast, small-area processor capable of
executing multiplication, division and square-root
operations, all starting from MSD is proposed. Unlike
the existing designs which require both addition and
subtraction operations, and complicated \ldots{}",
}
@Article{Das:1995:IFC,
author = "D. Das and K. Mukhopadhyaya and B. P. Sinha",
title = "Implementation of four common functions on an {LNS}
co-processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "155--161",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.367997",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We propose a scheme for evaluating four commonly used
functions namely, (1) inverse trigonometric functions,
(2) trigonometric functions, (3) the exponential
function, and (4) the logarithmic function with the
help of a logarithmic number system (\ldots{}).",
}
@Article{Daumas:1995:MRR,
author = "Marc Daumas and Christophe Mazenc and Xavier Merrheim
and Jean-Michel Muller",
title = "Modular range reduction: a new algorithm for fast and
accurate computation of the elementary functions",
journal = j-J-UCS,
volume = "1",
number = "3",
pages = "162--175 (electronic)",
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
MRclass = "68M07 (68Q20)",
MRnumber = "1 390 003",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Doman:1995:SAP,
author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
title = "A Set of {Ada} Packages for High Precision
Calculations",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "416--431",
month = dec,
year = "1995",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Nov 14 09:57:55 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "accuracy; Ada; arithmetic elementary-function
evaluation; floating-point; multiple-precision portable
software",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic; G.1.2 [Numerical Analysis]: Approximation
-- elementary function approximation; G.4 [Mathematics
of Computing]: Mathematical Software -- algorithm
analysis; efficiency; portability",
}
@Article{Goano:1995:ACC,
author = "Michele Goano",
title = "{Algorithm 745}: Computation of the Complete and
Incomplete {Fermi--Dirac} Integral",
journal = j-TOMS,
volume = "21",
number = "3",
pages = "221--232",
month = sep,
year = "1995",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/210089.210090",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Mar 09 10:19:43 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Goano:1997:RA7}",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "asymptotic expansions; confluent hypergeometric
functions; convergence acceleration; e[k] transforms;
epsilon algorithm; Euler transformation; Fermi--Dirac
integral; incomplete Fermi--Dirac integral; incomplete
gamma function; Levin's u transform; Riemann's zeta
function",
subject = "G.1.2 [Mathematics of Computing]: Approximation; G.4
[Mathematics of Computing]: Mathematical Software; J.2
[Computer Applications]: Physical Sciences and
Engineering",
}
@Article{Hobson:1995:EMR,
author = "R. F. Hobson and M. W. Fraser",
title = "An efficient maximum-redundancy radix-$8$ {SRT}
division and square-root method",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "30",
number = "1",
pages = "29--38",
month = jan,
year = "1995",
CODEN = "IJSCBC",
DOI = "http://dx.doi.org/10.1109/4.350197",
ISSN = "0018-9200",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the next quotient or
square-root digit by the divisor or square-root value.
A separate (parallel) full precision iterative
multiplier is used for partial remainder production.
Strategic details of a radix-8 implementation are
discussed. It is shown that a maximally redundant digit
set is a viable choice for high performance in this
case.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
Canada",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5230 (Digital arithmetic methods)",
keywords = "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
floating point algorithm; Integrated control path;
Maximally redundant digit set; Maximum-redundancy
radix-8 SRT algorithm; Multiplication; Parallel
iterative multiplier; Partial remainder production;
Redundant partial-remainder; Square-root method; Table
lookup",
language = "English",
numericalindex = "Size 1.2E-06 m",
pubcountry = "USA",
summary = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the \ldots{}",
thesaurus = "Adders; CMOS digital integrated circuits; Digital
arithmetic; Dividing circuits; Floating point
arithmetic; Multiplying circuits",
}
@InProceedings{Ito:1995:EIA,
author = "M. Ito and N. Takagi and S. Yajima",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Efficient Initial Approximation and Fast Converging
Methods for Division and Square Root",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2--9",
month = jul,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "Efficient initial approximations and fast converging
algorithms are important to achieve the desired
precision faster at lower hardware cost in
multiplicative division and square root. In this paper,
a new initial approximation method for division,
\ldots{}",
}
@Article{Krattenthaler:1995:HHM,
author = "C. Krattenthaler",
title = "{HYP} and {HYPQ}: {Mathematica} packages for the
manipulation of binomial sums and hypergeometric
series, respectively $q$-binomial sums and basic
hypergeometric series",
journal = j-J-SYMBOLIC-COMP,
volume = "20",
number = "5--6",
pages = "737--744",
month = nov # "--" # dec,
year = "1995",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
MRclass = "05Axx (11Bxx 33-04 33Cxx 33Dxx)",
MRnumber = "1 395 424",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Symbolic computation in combinatorics $\Delta_1$
(Ithaca, NY, 1993).",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics computing); C1100 (Mathematical
techniques)",
corpsource = "Inst. fur Math., Wien Univ., Austria",
keywords = "basic hypergeometric; binomial sums; HYP;
hypergeometric series; HYPQ; Mathematica packages;
mathematics computing; packages; q-binomial sums;
series; series (mathematics); software; symbol
manipulation",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kwan:1995:CII,
author = "H. Kwan and R. L. {Nelson, Jr.} and E. E.
{Swartzlander, Jr.}",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Cascaded Implementation of an Iterative
Inverse-Square-Root Algorithm, with Overflow
Lookahead",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "115--122",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "We present an unconventional method of computing the
inverse of the square root. It implements the
equivalent of two iterations of a well-known
multiplicative method to obtain 24-bit mantissa
accuracy. We implement each ``iteration'' as a
\ldots{}",
}
@InProceedings{Lang:1995:VHR,
author = "T. Lang and P. Montuschi",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Very-High Radix Combined Division and Square Root with
Prescaling and Selection by Rounding",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "124--131",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root with prescaling is
developed and combined with a similar scheme for
division. An implementation is described, evaluated and
compared with other combined div/sqrt \ldots{}",
}
@Book{Lau:1995:NLC,
author = "H. T. (Hang Tong) Lau",
title = "A Numerical library in {C} for scientists and
engineers",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xvii + 795",
year = "1995",
ISBN = "0-8493-7376-X",
ISBN-13 = "978-0-8493-7376-3",
LCCN = "QA76.73.C15 L38 1995",
bibdate = "Fri Sep 26 14:29:10 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
acknowledgement = ack-nhfb,
subject = "C (Computer program language)",
}
@InProceedings{Leeser:1995:VSR,
author = "M. Leeser and J. O'Leary",
booktitle = "Proceedings of the IEEE International Conference on
Computer Design: VLSI in Computers and Processors, ICCD
'95",
title = "Verification of a subtractive radix-$2$ square root
algorithm and implementation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "526--531",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Many modern microprocessors implement floating point
square root hardware using subtractive algorithms. Such
processors include the HP PA7200, the MIPS R4400, and
the Intel Pentium. The Intel Pentium division bug
highlights the importance of \ldots{}",
}
@Article{Lewanowicz:1995:AMC,
author = "Stanis{\l}aw Lewanowicz and Stefan Paszkowski",
title = "An analytic method for convergence acceleration of
certain hypergeometric series",
journal = j-MATH-COMPUT,
volume = "64",
number = "210",
pages = "691--713",
month = apr,
year = "1995",
CODEN = "MCMPAF",
DOI = "http://dx.doi.org/10.2307/2153446",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C45 (65B10 65D20)",
MRnumber = "1277769 (95h:33006)",
MRreviewer = "Anton Hut'a",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
classcodes = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
fjournal = "Mathematics of Computation",
keywords = "analytic method; convergence acceleration; convergence
of numerical methods; fast converging expansions;
hypergeometric; iterated transformation; mathematical
constants; series; series (mathematics)",
treatment = "T Theoretical or Mathematical",
}
@Article{Liu:1995:SRV,
author = "S.-I. Liu",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G - Circuits, Devices and
Systems]",
volume = "142",
number = "4",
pages = "223--226",
month = aug,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "New analogue squaring, square-rooting and vector
summation circuits using current conveyors (CCIIs) are
presented. They consist of MOS transistors biased in
the triode region, a buffered unity-gain inverting
amplifier, resistors and CCIIs. A general \ldots{}",
}
@Article{Louie:1995:VPS,
author = "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
title = "A Variable-Precision Square Root Implementation for
Field Programmable Gate Arrays",
journal = j-J-SUPERCOMPUTING,
volume = "9",
number = "3",
pages = "315--336",
month = sep,
year = "1995",
CODEN = "JOSUED",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01212874",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 11:13:09 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jsuper.bib;
http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
http://www.wkap.nl/oasis.htm/95692",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., California Univ., Los Angeles,
CA, USA",
classification = "C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
corpsource = "Dept. of Comput. Sci., California Univ., Los Angeles,
CA, USA",
fjournal = "The Journal of Supercomputing",
keywords = "digital arithmetic; field programmable gate arrays;
square root; square root implementation;
variable-precision; Xilinx XC4010",
treatment = "P Practical",
}
@Article{Lucas:1995:EII,
author = "S. K. Lucas and H. A. Stone",
title = "Evaluating infinite integrals involving {Bessel}
functions of arbitrary order",
journal = j-J-COMP-APPL-MATH,
volume = "64",
number = "3",
pages = "217--231",
year = "1995",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/0377-0427(95)00142-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Thu Jul 8 13:22:49 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452",
acknowledgement = ack-nhfb,
keywords = "$\varepsilon$-algorithm; Bessel functions; Bessel
zeros; infinite integration; mW transform; quadrature",
remark = "This paper examines several methods for accurately
integrating oscillatory functions, such as products of
$f(x)$ with a trigonometric function or a Bessel
function. It also discusses finding zeros of Bessel
functions, and sequence acceleration techniques.",
}
@Article{Luther:1995:HAT,
author = "Wolfram Luther",
title = "Highly accurate tables for elementary functions",
journal = j-BIT-NUM-MATH,
volume = "35",
number = "3",
pages = "352--360",
month = sep,
year = "1995",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01732609",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20 (68U05)",
MRnumber = "97h:65024",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit35.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@InProceedings{Lynch:1995:KTF,
author = "T. Lynch and A. Ahmed and M. Schulte and T. Callaway",
title = "The {K5} Transcendental Functions",
crossref = "Knowles:1995:PSC",
pages = "163--171",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Matsubara:1995:NBS,
author = "G. Matsubara and N. Ide and H. Tago and S. Suzuki and
N. Goto",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "30-ns 55-b Shared Radix $2$ Division and Square Root
Using a Self-Timed Circuit",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "98--105",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "A shared radix 2 division and square root
implementation using a self-timed circuit is presented.
The same execution time for division and square root is
achieved by using an on-the-fly digit decoding and a
root multiple generation technique. Most \ldots{}",
}
@Article{Montuschi:1995:RRI,
author = "P. Montuschi and L. Ciminiera",
title = "A remark on {``Reducing iteration time when result
digit is zero for radix-$2$ {SRT} division and square
root with redundant remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "144--146",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.368000",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Montuschi:1993:RIT}.",
acknowledgement = ack-nhfb,
summary = "In a previous paper by P. Montuschi and L. Ciminiera
(ibid., vol. 42, no.2 p239-246, Feb 1993), an
architecture for shared radix 2 division and square
root has been presented whose main characteristic is
the ability to avoid any addition/subtraction,
\ldots{}",
}
@Article{OLeary:1995:NRI,
author = "J. O'Leary and M. Leeser and J. Hickey and M.
Aagaard",
title = "Non-Restoring Integer Square Root: {A} Case Study in
Design by Principled Optimization",
journal = j-LECT-NOTES-COMP-SCI,
volume = "901",
pages = "52--??",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
bibdate = "Sat May 11 13:45:32 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Paszkowski:1995:QHS,
author = "S. Paszkowski",
title = "Quasipower and hypergeometric series---construction
and evaluation",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "3--4",
pages = "337--361",
month = oct,
year = "1995",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "41A58 (33-04 65B99)",
MRnumber = "96k:41042",
MRreviewer = "Walter Schempp",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290Z (Other numerical methods); C4130 (Interpolation
and function approximation); C4190 (Other numerical
methods)",
corpsource = "Inst. for Low Temp. and Structure Res., Polish Acad.
of Sci., Wroclaw, Poland",
keywords = "approximation theory; Euler's dilogarithm;
Hermite-Pade approximation; hypergeometric series;
Levin's transforms; Pade approximants; power series;
quasipower; recurrence relations; series (mathematics);
transforms",
pubcountry = "Switzerland",
treatment = "P Practical; T Theoretical or Mathematical",
}
@InProceedings{Prabhu:1995:MRD,
author = "J. A. Prabhu and G. B. Zyner",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "{167 MHz} Radix-$8$ Divide and Square Root Using
Overlapped Radix-$2$ Stages",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "155--162",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "UltraSPARC's IEEE-754 compliant floating point divide
and square root implementation is presented. Three
overlapping stages of SRT radix-$2$ quotient selection
logic enable an effective radix-$8$ calculation at 167
MHz while only a single radix-$2$ \ldots{}",
}
@InProceedings{Schwarz:1995:RQC,
author = "E. M. Schwarz",
booktitle = "Conference Record of the Twenty-Ninth Asilomar
Conference on Signals, Systems and Computers, 1995",
title = "Rounding for quadratically converging algorithms for
division and square root",
crossref = "Singh:1995:CRT",
volume = "1",
pages = "600--603",
month = oct,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "Exactly rounded results are necessary for many
architectures such as IEEE 754 standard. For division
and square root, rounding is easy to perform if a
remainder is available. But for quadratically
converging algorithms, the remainder is not \ldots{}",
}
@Article{Sidhu:1995:EIF,
author = "Satinder S. Sidhu",
title = "Elliptic Integrals and Functions",
journal = j-COMP-PHYSICS,
volume = "9",
number = "3",
pages = "268--276",
month = may # "\slash " # jun,
year = "1995",
CODEN = "CPHYE2",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Thu Feb 02 18:05:53 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers in Physics",
}
@Article{Smith:1995:CFA,
author = "Roger Alan Smith",
title = "A Continued-Fraction Analysis of Trigonometric
Argument Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "11",
pages = "1348--1351",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.475133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Dec 08 10:21:28 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The calculation of a trigonometric function of a large
argument x is effectively carried out by finding the
integer $N$ and $0 \leq \alpha < 1$ such that $x = (N +
\alpha) \pi/4$. This reduction modulo $\pi/4$ makes it
possible to calculate a trigonometric function of a
reduced argument, either $\alpha\pi/4$ or $(1 -
\alpha)\pi/4$, which lies in the interval $(0, \pi/4)$.
Payne and Hanek [1] described an efficient algorithm
for computing $\alpha$ to a predetermined level of
accuracy. They noted that if $x$ differs only slightly
from an integral multiple $\pi/2$, the reduction must
be carried out quite accurately to avoid loss of
significance in the reduced argument. We present a
simple method using continued fractions for
determining, for all numbers $x$ for which the greatest
number of insignificant leading bits occur.
Applications are made IEEE single-precision and
double-precision formats and two extended- precision
formats.",
acknowledgement = ack-nhfb,
keywords = "argument reduction; computer arithmetic; continued
fractions; nonlinear optimization; Payne/Hanek radian
reduction; range reduction; trigonometric functions",
}
@InProceedings{Soderquist:1995:APC,
author = "Peter Soderquist and Miriam Leeser",
title = "An Area\slash Performance Comparison of Subtractive
and Multiplicative Divide\slash Square Root
Implementations",
crossref = "Knowles:1995:PSC",
pages = "132--139",
month = jul,
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12",
}
@Book{Varchenko:1995:MHF,
author = "A. N. (Aleksandr Nikolaevich) Varchenko",
title = "Multidimensional hypergeometric functions and
representation theory of {Lie} algebras and quantum
groups",
volume = "21",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "ix + 371",
year = "1995",
ISBN = "981-02-1880-X",
ISBN-13 = "978-981-02-1880-5",
LCCN = "QA353.H9 V37 1995",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Advanced series in mathematical physics",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Kac-Moody algebras;
Representations of Lie algebras; Representations of
quantum groups",
}
@Book{Vilenkin:1995:RLG,
author = "N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii
Ulsianovich) Klimyk",
title = "Representation of {Lie} groups and special functions:
recent advances",
volume = "316",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvi + 497",
year = "1995",
ISBN = "0-7923-3210-5",
ISBN-13 = "978-0-7923-3210-7",
LCCN = "QA176 .V55 1995",
bibdate = "Sat Oct 30 16:43:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematics and its applications",
URL = "http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html;
http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html",
acknowledgement = ack-nhfb,
remark = "Translated to English from Russian by V. A. Groza and
A. A. Groza.",
subject = "Representations of Lie groups; Functions, Special;
Integral transforms",
}
@Article{Vrahatis:1995:RPP,
author = "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
Zafiropoulos and T. N. Grapsa",
title = "{RFSFNS}: a portable package for the numerical
determination of the number and the calculation of
roots of {Bessel} functions",
journal = j-COMP-PHYS-COMM,
volume = "92",
number = "2--3",
pages = "252--266",
month = dec,
year = "1995",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:01 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
note = "See erratum \cite{Vrahatis:1999:ESP}.",
URL = "http://www.sciencedirect.com/science/article/pii/0010465595001159",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Wong:1995:EHS,
author = "W. F. Wong and Yoshio Oyanagi and Eiichi Goto",
title = "Evaluation of the {Hitachi S-3800} Supercomputer Using
Six Benchmarks",
journal = j-IJSAHPC,
volume = "9",
number = "1",
pages = "58--70",
month = "Spring",
year = "1995",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibdate = "Tue Feb 18 09:07:32 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The S-3000 series is the third generation of Hitachi's
supercomputers. It is claimed to be currently the
fastest single processor supercomputer. In this paper,
we introduce the S-3000 and, using six benchmarks we
designed, evaluate a member of this series of
supercomputer, the top of the range S-3800, against its
predecessor, the Hitachi HITAC S-820. Our purpose is to
determine in what areas the S-3800 is an improvement
over its predecessor. The suite of benchmarks include
kernels for random number generation, elementary
function computation, FFT, dense matrix operations,
SOR, and list vector (scatter\slash gather) operations.
The use of small-to medium-sized kernels, as opposed to
large application benchmarks, help to better understand
the behavior of the machine. Our findings support the
claim that the S-3000 series is at least twice as fast
as the previous generation of Hitachi supercomputers.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore",
affiliationaddress = "Singapore",
classification = "722.4; 921.3; 921.6; 922.2",
journalabr = "Int J Supercomput Appl High Perform Comput",
keywords = "Benchmarks; Computer selection and evaluation;
Computer testing; Fast Fourier transforms; Fastest
single processor; Hitachi supercomputer; Matrix
algebra; Medium sized kernels; Performance; Random
number generation; Supercomputers; Vectors",
}
@Article{Wong:1995:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in single
precision",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "3",
pages = "453--457",
month = mar,
year = "1995",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.372037",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In this paper we introduce a new method for the fast
evaluation of the elementary functions in single
precision based on the evaluation of truncated Taylor
series using a difference method. We assume the
availability of large and fast (at least for read
purposes) memory. We call this method the ATA
(Add-Table lookup-Add) method. As the name implies, the
hardware required for the method are adders (both two/
and multi/operand adders) and fast tables. For IEEE
single precision numbers our initial estimates indicate
that we can calculate the basic elementary functions,
namely reciprocal, square root, logarithm, exponential,
trigonometric and inverse trigonometric functions,
within the latency of two to four floating point
multiplies.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
keywords = "Adders; Difference method; Elementary functions; Fast
evaluation; Floating point multiplies; Inverse
trigonometric functions; Logarithm functions;
Reciprocal; Single precision; Square root; Truncated
Taylor series",
language = "English",
pubcountry = "USA",
thesaurus = "Error analysis; Floating point arithmetic",
}
@Article{Zhang:1995:TMAa,
author = "J. Zhang and J. A. Belward",
title = "Tau-method approximations for the {Bessel} function
{$Y_0(z)$}",
journal = j-COMP-MATH-APPL,
volume = "30",
number = "7",
pages = "5--14",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(95)00120-N",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 08:33:42 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500120N",
acknowledgement = ack-nhfb,
}
@Article{Zhang:1995:TMAb,
author = "J. Zhang",
title = "Tau-method approximations for the {Bessel} function
{$Y_1(z)$}",
journal = j-COMP-MATH-APPL,
volume = "30",
number = "7",
pages = "15--19",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/Sun Jun 12 09:25:24 2011",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 09:26:01 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500121E",
acknowledgement = ack-nhfb,
remark = "From p. 18 (conclusions section), ``We may use this
method to approximate the Bessel functions of other
integer orders. \ldots{} It is therefore advisable to
use the recurrence relations of the Bessel functions to
compute function values for $n > 1$ \ldots''. [This is
a similar limitation as with Chebyshev and minimax
polynomial approximations: they are valid only for a
single order the Bessel function.]",
}
@InProceedings{Ahrendt:1996:FHC,
author = "Timm Ahrendt",
title = "Fast High-Precision Computations of Complex Square
Roots",
crossref = "LakshmanYN:1996:IPI",
pages = "142--149",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; measurement;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Bounded-action devices.
{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Iterative
methods. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
xxtitle = "Fast high-precision computation of complex square
roots",
}
@Article{Cappuccino:1996:DDH,
author = "G. Cappuccino and P. Corsonello and G. Cocorullo",
title = "Design and demonstration of high throughput square
rooting circuit",
journal = j-ELECT-LETTERS,
volume = "32",
number = "5",
pages = "434",
month = "????",
year = "1996",
CODEN = "ELLEAK",
ISSN = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@InProceedings{Guyot:1996:STD,
author = "A. Guyot and M. Renaudin and B. {El Hassan} and V.
Levering",
booktitle = "Proceedings of the Ninth International Conference on
VLSI Design, 1996",
title = "Self timed division and square-root extraction",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "376--381",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes a self-timed integrated circuit
for division and square-root extraction. First it
concentrates on the development and the proof of a new
mathematical algorithm. Then the design methodology and
the architecture of a self-timed \ldots{}",
}
@Article{Heinrich:1996:AAF,
author = "Peter Heinrich",
title = "Algorithm Alley: {A} Fast Integer Square Root",
journal = j-DDJ,
volume = "21",
number = "4",
pages = "113--114, 130",
month = apr,
year = "1996",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Hickey:1996:FSP,
author = "Timothy J. Hickey and Qun Ju",
title = "Fast, Sound, and Precise Narrowing of the Exponential
Function",
type = "Technical report",
institution = "Computer Science Department, Brandeis University",
address = "Waltham, MA, USA 02254",
month = mar,
year = "1996",
bibdate = "Sat Nov 05 15:42:23 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{Homeier:1996:CAI,
author = "H. H. H. Homeier",
title = "On Convergence Acceleration for the Iterative Solution
of the Inverse {Dyson} Equation",
journal = j-J-MOL-STRUCT-THEOCHEM,
volume = "368",
pages = "81--91",
year = "1996",
CODEN = "THEODJ",
ISSN = "0166-1280 (print), 1872-7999 (electronic)",
ISSN-L = "0166-1280",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the 2nd {Electronic Computational
Chemistry Conference}.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
fjournal = "Journal of molecular structure. Theochem",
keywords = "convergence acceleration",
tech = "Technical Report TC-QM-95-4, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}
@TechReport{Homeier:1996:KMP,
author = "H. H. H. Homeier",
title = "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
St{\"o}rungsreihe} ({English}: {On} Convergence
Acceleration of the {M{\o}ller--Plesset} Perturbation
Series)",
number = "Homeier:1996:KMP",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Poster CP 14.77, {Fr{\"u}hjahrstagung des
Arbeitskreises Festk{\"o}rperphysik bei der DPG,
Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
2165-2166 (1996).",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
keywords = "convergence acceleration",
}
@Article{Ito:1996:SRI,
author = "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
title = "Square rooting by iterative multiply-additions",
journal = j-INFO-PROC-LETT,
volume = "60",
number = "5",
pages = "267--269",
day = "8",
month = dec,
year = "1996",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07",
MRnumber = "97i:68014",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
corpsource = "Dept. of Inf. Sci., Kyoto Univ., Japan",
keywords = "computer arithmetic; convergence of numerical methods;
digital arithmetic; iterative methods; iterative
multiply-additions; linear converging ratio;
multiplicative methods; Newton--Raphson method;
read-only storage; ROM sizes; square root algorithm",
treatment = "T Theoretical or Mathematical",
}
@Unpublished{Kahan:1996:TCR,
author = "W. Kahan",
title = "A Test for Correctly Rounded {SQRT}",
pages = "4",
year = "1996",
bibdate = "Mon Apr 25 05:47:38 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Lecture notes.",
URL = "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Kalantari:1996:HOI,
author = "B. Kalantari and I. Kalantari",
title = "High order iterative methods for approximating square
roots",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "2",
pages = "395--399",
month = jun,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01731991",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D15 (65H99)",
MRnumber = "97k:65039",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
acknowledgement = ack-nhfb,
}
@Article{Kantabutra:1996:HCE,
author = "V. Kantabutra",
title = "On hardware for computing exponential and
trigonometric functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "3",
pages = "328--339",
month = mar,
year = "1996",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.485571",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:09 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Lehoucq:1996:CEU,
author = "R. B. Lehoucq",
title = "The Computation of Elementary Unitary Matrices",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "393--400",
month = dec,
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The construction of elementary unitary matrices that
transform a complex vector to a multiple of $e_1$, the
first column of the identity matrix, is studied. We
present four variants and their software
implementation, including a discussion on the {LAPACK}
subroutine {CLARFG}. Comparisons are also given.",
accepted = "June 1996",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
keywords = "algorithms",
subject = "{\bf F.2}: Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.1.3}:
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis.",
}
@InProceedings{Li:1996:NNR,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the IEEE International Conference on
Computer Design: VLSI in Computers and Processors: ICCD
'96",
title = "A new non-restoring square root algorithm and its
{VLSI} implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "538--544",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present a new non-restoring square root algorithm
that is very efficient to implement. The new algorithm
presented here has the following features unlike other
square root algorithms. First, the focus of the
``non-restoring'' is on the {\&} \ldots{}",
}
@TechReport{Lozier:1996:PST,
author = "Daniel W. Lozier",
title = "A Proposed Software Test Service for Special
Functions",
type = "Technical Report",
number = "NISTIR 5916",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "11",
month = oct,
year = "1996",
bibdate = "Fri Jul 09 06:02:16 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Lozier:1997:PST}.",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
acknowledgement = ack-nhfb,
}
@Article{Lozier:1996:SNS,
author = "Daniel W. Lozier",
title = "Software Needs in Special Functions",
journal = j-J-COMP-APPL-MATH,
volume = "66",
number = "??",
pages = "345--358",
month = "????",
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Fri Jul 09 05:51:55 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "See preprint \cite{Lozier:1994:SNS}.",
}
@Article{Macleod:1996:AMS,
author = "Allan J. Macleod",
title = "{Algorithm 757}: {MISCFUN}, a software package to
compute uncommon special functions",
journal = j-TOMS,
volume = "22",
number = "3",
pages = "288--301",
month = sep,
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 31 16:07:02 MDT 1996",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://doi.acm.org/10.1145/232826.232846;
http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
abstract = "MISCFUN (MISCellaneous FUNctions) is a Fortran package
for the evaluation of several special functions, which
are not used often enough to have been included in the
standard libraries or packages. The package uses
Chebyshev expansions as the underlying method of
approximation, with the Chebyshev coefficients given to
20D. A wide variety of functions are included, and the
package is designed so that other functions can be
added in a standard manner.",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Certification and
testing.",
}
@Article{Oleksy:1996:CAM,
author = "Cz. Oleksy",
title = "A convergence acceleration method of {Fourier}
series",
journal = j-COMP-PHYS-COMM,
volume = "96",
number = "1",
pages = "17--26",
year = "1996",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/0010-4655(96)00044-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65B05",
MRnumber = "1396682 (97c:65012)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
keywords = "convergence acceleration",
}
@Article{Qiu:1996:SEC,
author = "S.-L. Qiu and M. K. Vamanamurthy",
title = "Sharp Estimates for Complete Elliptic Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "27",
number = "3",
pages = "823--834",
month = may,
year = "1996",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05",
MRnumber = "97f:33033",
MRreviewer = "G. D. Anderson",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rao:1996:RTS,
author = "V. M. Rao and B. Nowrouzian",
booktitle = "Canadian Conference on Electrical and Computer
Engineering. 26--29 May 1996",
title = "Rounding techniques for signed binary arithmetic",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "294--297",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This paper is concerned with the derivation of the
relationship that exists between the number truncation
in two's complement (TC) arithmetic and the
corresponding truncation in signed-binary (SB)
arithmetic. The resulting relationship is subsequently
exploited and applied to the development of a pair of
novel techniques for SB rounding. These techniques are
then translated into algorithm suitable for two-level
logic implementation. Finally, the resulting algorithms
are applied to the design and implementation of a
high-speed SB-kernel based TC multiply-accumulate
arithmetic architecture.",
acknowledgement = ack-nhfb,
}
@Article{Schwarz:1996:HSA,
author = "Eric M. Schwarz and Michael J. Flynn",
title = "Hardware Starting Approximation Method and Its
Application to the Square Root Operation",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "12",
pages = "1356--1369",
month = dec,
year = "1996",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.545966",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Quadratically converging algorithms for high-order
arithmetic operations typically are accelerated by a
starting approximation. The higher the precision of the
starting approximation, the less number of iterations
required for convergence. \ldots{}",
}
@Article{Sinclair:1996:ORS,
author = "R. Sinclair",
title = "Optimization of reciprocals and square roots on the
{i860} microprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "8",
number = "1",
pages = "57--64",
year = "1996",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibdate = "Mon Feb 25 11:19:22 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Article1st database",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing
(IJHSC)",
}
@Book{Temme:1996:SFI,
author = "N. M. Temme",
title = "Special functions: an introduction to the classical
functions of mathematical physics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 374",
year = "1996",
ISBN = "0-471-11313-1",
ISBN-13 = "978-0-471-11313-3",
LCCN = "QC20.7.F87 T46 1996",
bibdate = "Mon Nov 24 21:41:54 MST 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "functions, special; mathematical physics; boundary
value problems",
}
@Book{Walz:1996:AE,
author = "Guido Walz",
title = "Asymptotics and extrapolation",
volume = "88",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "330",
year = "1996",
ISBN = "3-05-501732-3",
ISBN-13 = "978-3-05-501732-2",
LCCN = "QA281 .W349 1996",
bibdate = "Thu Dec 1 10:25:13 MST 2011",
bibsource = "catalog.princeton.edu:7090/voyager;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematical research",
acknowledgement = ack-nhfb,
subject = "Extrapolation; Asymptotic expansions",
}
@Article{Williams:1996:TMF,
author = "K. B. Williams",
title = "Testing Math Functions: When requirements are tight,
we must carefully examine all potential sources of
error. {Make} sure your math library isn't the weak
link in the chain",
journal = j-CCCUJ,
volume = "14",
number = "12",
pages = "49--54, 58--65",
month = dec,
year = "1996",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Thu Nov 14 06:34:33 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Describes a package that extends the
Cody-Waite-Plauger work on the ELEFUNT package for the
testing of the elementary functions, including the
inverse hyperbolic functions, cube root, and Bessel
functions of the first and second kinds. The C++
package implements 192-bit extended precision versions
of all of the functions, so that accurate results are
available for comparison with the normal
double-precision results.",
acknowledgement = ack-nhfb,
}
@Book{Zhang:1996:CSF,
author = "Shanjie Zhang and Jianming Jin",
title = "Computation of special functions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xxvi + 717",
year = "1996",
ISBN = "0-471-11963-6",
ISBN-13 = "978-0-471-11963-0",
LCCN = "QA351.C45 1996",
bibdate = "Wed Mar 22 14:39:04 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$94.00",
acknowledgement = ack-nhfb,
tableofcontents = "Bernoulli and Euler Numbers \\
Orthogonal Polynomials \\
Gamma, Beta, and Psi Functions \\
Legendre Functions \\
Bessel Functions \\
Modified Bessel Functions \\
Integrals of Bessel Functions \\
Spherical Bessel Functions \\
Kelvin Functions \\
Airy Functions \\
Struve Functions \\
Hypergeometric and Confluent Hypergeometric Functions
\\
Parabolic Cylinder Functions \\
Mathieu Functions \\
Spheroidal Wave Functions \\
Error Function and Fresnel Integrals \\
Cosine and Sine Integrals \\
Elliptic Integrals and Jacobian Elliptic Functions \\
Exponential Integrals \\
Summary of Methods for Computing Special Functions \\
Appendices \\
Indexes",
xxauthor = "Shan-chieh Chang and Shanjie Zhang and Jianming Jin",
xxnote = "There is online bookstore and library catalog
confusion over the authors of this book. The
publisher's Web page at
http://catalog.wiley.com/remsrch.cgi has Shan-jie Zhang
(Nanjing Univ., China) / Jianming Jin (Univ. of
Illinois at Urbana-Champaign), and a price of
US\$125.00. It looks like Shan-chieh Chang is merely a
different English transcription of Shanjie Zhang.
http://www.fatbrain.com/ lists this book for US\$99.95.
My copy of the book lists the authors as Shanjie Zhang
and Jianming Jin in four places.",
}
@Article{Zhang:1996:NTM,
author = "J. Zhang",
title = "A note on the tau-method approximations for the
{Bessel} functions {$Y_0(z)$} and {$Y_1(z)$}",
journal = j-COMP-MATH-APPL,
volume = "31",
number = "9",
pages = "63--70",
month = may,
year = "1996",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/0898-1221(96)00043-0",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 08:43:36 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122196000430",
abstract = "This paper is to complete and improve the work
reported in [1,2], using the Lanczos $\tau$-method (in
Coleman's version) to approximate the Bessel functions
$Y_0(z)$ and $Y_1(z)$. We introduce symbolic
representations of the scaled Faber polynomials on any
fan-shaped section of the complex plane. These Faber
polynomials are used as the perturbation terms in the
$\tau$-method. Numerical comparison among the power
series, the Chebyshev series and the $\tau$-method are
conducted to show the accuracy improvement achieved by
this new version of the $\tau$-method. Some concluding
remarks and suggestions on future research are given.",
acknowledgement = ack-nhfb,
keywords = "Automated $\tau$-method; Bessel functions; Chebyshev
series; Symbolic Faber polynomials",
}
@Article{Alzer:1997:SIG,
author = "Horst Alzer",
title = "On some inequalities for the gamma and psi functions",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "373--389",
month = jan,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33B15 (26D07)",
MRnumber = "97e:33004",
MRreviewer = "Peter Schroth",
bibdate = "Fri Jul 16 10:38:40 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-217;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
acknowledgement = ack-nhfb,
}
@Article{Alzer:1997:SII,
author = "Horst Alzer",
title = "On some inequalities for the incomplete gamma
function",
journal = j-MATH-COMPUT,
volume = "66",
number = "218",
pages = "771--778",
month = apr,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33B20 (26D07)",
MRnumber = "97h:33004",
bibdate = "Fri Jul 16 10:38:42 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-218;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
acknowledgement = ack-nhfb,
}
@Article{Blinn:1997:JBC,
author = "James F. Blinn",
title = "{Jim Blinn}'s Corner: Floating-Point Tricks",
journal = j-IEEE-CGA,
volume = "17",
number = "4",
pages = "80--84",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "ICGADZ",
DOI = "http://dx.doi.org/10.1109/38.595279",
ISSN = "0272-1716 (print), 1558-1756 (electronic)",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Discusses use of IEEE 754 single-precision
floating-point bit patterns as integers for
implementations of fast, but low-accuracy, functions
useful in computer graphics.",
acknowledgement = ack-nhfb,
summary = "The author discusses IEEE floating point
representation that stores numbers in what amounts to
scientific notation. He considers the sign bit, the
logarithm function, function approximations, errors and
refinements \ldots{}",
}
@Article{Bshouty:1997:TBA,
author = "Nader H. Bshouty and Yishay Mansour and Baruch
Schieber and Prasoon Tiwari",
title = "A tight bound for approximating the square root",
journal = j-INFO-PROC-LETT,
volume = "63",
number = "4",
pages = "211--213",
day = "10",
month = sep,
year = "1997",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68Q25 (65B15 68Q40)",
MRnumber = "1 477 306",
bibdate = "Sat Nov 7 17:55:54 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fdil:1997:SRC,
author = "A. Fdil",
title = "Some results of convergence acceleration for a general
${\Theta}$-type algorithm",
journal = j-APPL-NUM-MATH,
volume = "23",
number = "2",
pages = "219--240",
day = "21",
month = mar,
year = "1997",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
MRclass = "65B10 (65D32)",
MRnumber = "1 437 884",
bibdate = "Wed Jul 28 14:36:42 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Forrey:1997:CHF,
author = "Robert C. Forrey",
title = "Computing the hypergeometric function",
journal = j-J-COMPUT-PHYS,
volume = "137",
number = "1",
pages = "79--100",
month = oct,
year = "1997",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1006/jcph.1997.5794",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "33C05 (33-04 65D20)",
MRnumber = "MR1481885 (99g:33004)",
bibdate = "Thu Dec 01 09:06:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
remark = "The author gives a FORTRAN program for computing
$_2F_1$ for real variable and parameters, using
rapidly-convergent power series in six separate
intervals.",
}
@Article{Ghanem:1997:SBF,
author = "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
title = "Spherical {Bessel} functions and explicit quadrature
formula",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "289--296",
month = jan,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "33C10 (41A55 65D32)",
MRnumber = "97c:33005",
MRreviewer = "N. Hayek Calil",
bibdate = "Fri Jul 16 10:38:40 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-217;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
acknowledgement = ack-nhfb,
}
@Article{Goano:1997:RA7,
author = "Michele Goano",
title = "Remark on {Algorithm 745}",
journal = j-TOMS,
volume = "23",
number = "2",
pages = "295--295",
month = jun,
year = "1997",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/264029.643581",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Mar 9 10:19:38 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Goano:1995:ACC}.",
acknowledgement = ack-rfb # " and " # ack-kr # "\slash " # ack-nhfb,
}
@Article{Hare:1997:CPB,
author = "D. E. G. Hare",
title = "Computing the Principal Branch of {log-Gamma}",
journal = j-J-ALG,
volume = "25",
number = "2",
pages = "221--236",
month = nov,
year = "1997",
CODEN = "JOALDV",
DOI = "http://dx.doi.org/10.1006/jagm.1997.0881",
ISSN = "0196-6774",
bibdate = "Thu Mar 27 14:31:42 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The log-Gamma function is an important special
function of mathematics, and its principal branch is
required in many applications. We develop here the
mathematics required to evaluate the principal branch
to arbitrary precision, including a new bound for the
error in Stirling's asymptotic series. We conclude with
a discussion of the implementation of the principal
branch of the log-Gamma function in the Maple symbolic
algebra system, starting with version Maple V, Release
3.",
acknowledgement = ack-nhfb,
}
@TechReport{Homeier:1997:CAL,
author = "H. H. H. Homeier",
title = "Convergence Acceleration of Logarithmically Convergent
Series Avoiding Summation",
number = "Homeier:1997:CAL",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "{\em Appl. Math. Lett.}, in press.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA978",
keywords = "convergence acceleration",
}
@TechReport{Homeier:1997:ECSa,
author = "H. H. H. Homeier",
title = "Extended Complex Series Methods for the Convergence
Acceleration of {Fourier} Series",
number = "Homeier:1997:ECSa",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "{\em J. Comput. Phys.}, submitted.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA973",
keywords = "convergence acceleration",
}
@TechReport{Homeier:1997:ECSb,
author = "H. H. H. Homeier",
title = "On an Extension of the Complex Series Method for the
Convergence Acceleration of Orthogonal Expansions",
number = "Homeier:1997:ECSb",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "{\em Numer. Math.}, submitted.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA974",
keywords = "convergence acceleration",
}
@TechReport{Homeier:1997:PAL,
author = "H. H. H. Homeier",
title = "On Properties and the Application of {Levin}-type
Sequence Transformations for the Convergence
Acceleration of {Fourier} Series",
number = "Homeier:1997:PAL",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "{\em Math. Comp.}, submitted.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA971",
keywords = "convergence acceleration",
}
@Article{Ito:1997:EIA,
author = "M. Ito and N. Takagi and S. Yajima",
title = "Efficient initial approximation for multiplicative
division and square root by a multiplication with
operand modification",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "4",
pages = "495--498",
month = apr,
year = "1997",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.588066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
summary = "An efficient initial approximation method for
multiplicative division and square root is proposed. It
is a modification of the piecewise linear
approximation. The multiplication and the addition
required for the linear approximation are replaced by
\ldots{}",
}
@Article{Karp:1997:HPD,
author = "Alan H. Karp and Peter Markstein",
title = "High-Precision Division and Square Root",
journal = j-TOMS,
volume = "23",
number = "4",
pages = "561--589",
month = dec,
year = "1997",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/279232.279237",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
abstract = "We present division and square root algorithms for
calculation with more bits than are handled by the
floating-point hardware. These algorithms avoid the
need to multiply two high-precision numbers, speeding
up the last iteration by as much as a factor of 10. We
also show how to produce the floating-point number
closest to the exact result with relatively few
additional operations.",
accepted = "June 1997",
acknowledgement = ack-rfb # " and " # ack-kr,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
keywords = "algorithms, performance, division, quad precision,
square root.",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic. G.4 [Mathematics of Computing]:
Mathematical Software.",
}
@Article{Kolbig:1997:TEH,
author = "K. S. K{\"o}lbig",
title = "Table errata: {\em Handbook of elliptic integrals for
engineers and scientists} [Second edition, Springer,
New York, 1971, {MR} {\bf 43} \#3506] by {P. F. Byrd}
and {M. D. Friedman}",
journal = j-MATH-COMPUT,
volume = "66",
number = "220",
pages = "1767--1767",
month = oct,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "44-00 (33-00)",
MRnumber = "1 434 945",
bibdate = "Tue Dec 2 11:25:56 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:1997:ISP,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 5th Annual IEEE Symposium on FPGAs
for Custom Computing Machines, 16--18 April 1997",
title = "Implementation of single precision floating point
square root on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "226--232",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The square root operation is hard to implement on
FPGAs because of the complexity of the algorithms. In
this paper, we present a non-restoring square root
algorithm and two very simple single precision floating
point square root implementations \ldots{}",
}
@InProceedings{Li:1997:PAI,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 1997 IEEE International Conference
on Computer Design: VLSI in Computers and Processors:
ICCD '97",
title = "Parallel-array implementations of a non-restoring
square root algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "690--695",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "In this paper we present a parallel-array
implementation of a new non-restoring square root
algorithm (PASQRT). The carry-save adder (CSA) is used
in the parallel array. The PASQRT has several features
unlike other implementations. First, it does \ldots{}",
}
@InCollection{Lozier:1997:PST,
author = "Daniel W. Lozier",
title = "A Proposed Software Test Service for Special
Functions",
crossref = "Boisvert:1997:QNS",
pages = "167--178",
year = "1997",
bibdate = "Fri Jul 09 06:00:46 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "See preprint \cite{Lozier:1996:PST}.",
}
@TechReport{Lozier:1997:TRN,
author = "Daniel W. Lozier",
title = "Toward a Revised {NBS} Handbook of Mathematical
Functions",
type = "Technical Report",
number = "NISTIR 6072",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "8",
month = sep,
year = "1997",
bibdate = "Fri Jul 09 06:35:07 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz",
acknowledgement = ack-nhfb,
}
@InProceedings{Matsubara:1997:LPZ,
author = "G. Matsubara and N. Ide",
booktitle = "Proceedings of the Third International Symposium on
Advanced Research in Asynchronous Circuits and Systems,
7--10 April 1997",
title = "A low power zero-overhead self-timed division and
square root unit combining a single-rail static circuit
with a dual-rail dynamic circuit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "198--209",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An asynchronous pipeline scheme that combines a low
power static circuit with a high-speed dual-rail
dynamic circuit is proposed. The scheme utilizes a
dual-rail circuit only in the critical path of an SRT
division and square root calculation unit. \ldots{}",
}
@Book{Muller:1997:EFA,
author = "Jean-Michel Muller",
title = "Elementary functions: algorithms and implementation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xv + 204",
year = "1997",
ISBN = "0-8176-3990-X",
ISBN-13 = "978-0-8176-3990-7",
LCCN = "QA331.M866 1997",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$59.95",
URL = "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
http://www.ens-lyon.fr/~jmmuller/book_functions.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1997:AFA,
author = "M. J. Schulte and James E. Stine",
title = "Accurate Function Approximations by Symmetric Table
Lookup and Addition",
crossref = "Thiele:1997:IIC",
pages = "144--153",
year = "1997",
bibdate = "Sun Mar 04 10:55:40 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1997:SBT,
author = "M. Schulte and J. Stine",
title = "Symmetric Bipartite Tables for Accurate Function
Approximation",
crossref = "Lang:1997:ISC",
pages = "175--183",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Segura:1997:CEM,
author = "J. Segura and P. Fern{\'a}ndez de C{\'o}rdoba and Yu.
L. Ratis",
title = "A code to evaluate modified {Bessel} functions based
on the continued fraction method",
journal = j-COMP-PHYS-COMM,
volume = "105",
number = "2--3",
pages = "263--272",
day = "1",
month = oct,
year = "1997",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(97)00069-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:19 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465597000696",
abstract = "We present an algorithm to evaluate the modified
Bessel functions $I\_nu$ and $K_\nu$ of integral and
half-integral order based on the calculation of the
continued fraction for the $I\_nu$'s, the Wronskian and
the application of forward recurrence relations for the
$K_\nu$'s and backward recurrence for the $I\_nu$'s.
The main feature of the algorithm is that it does not
require recalculations using normalization relations
nor trial values to start the recurrences; the code
evaluates in each step (already normalized) Bessel
functions. The accuracy of the method ($10^{-16}$ for
half-integral order and better than $2 \times 10^{-7}$
for integral order in our code) is limited only by the
precision in the initial values for the recurrence and
the maximum order available for a given value of the
argument is restricted only by the maximum real number
available in the computer.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Soderquist:1997:DSR,
author = "Peter Soderquist and Miriam Leeser",
title = "Division and Square Root: Choosing the Right
Implementation: Exploring the major design choices for
microprocessor implementations of floating-point
division and square root",
journal = j-IEEE-MICRO,
volume = "17",
number = "4",
pages = "56--66",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/40.612224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
URL = "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
}
@Book{Thompson:1997:ACMa,
author = "William J. (William Jackson) Thompson",
title = "Atlas for computing mathematical functions: an
illustrated guidebook for practitioners: with programs
in {C} and {Mathematica}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 903",
year = "1997",
ISBN = "0-471-00260-7 (cloth)",
ISBN-13 = "978-0-471-00260-4 (cloth)",
LCCN = "QA331.T385 1997",
bibdate = "Fri May 21 07:11:19 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "A Wiley-Interscience publication. Includes CD-ROM.",
keywords = "C (Computer program language); Functions -- Computer
programs; Mathematica (Computer program language);
Science -- Mathematics -- Computer programs",
}
@Book{Thompson:1997:ACMb,
author = "William J. (William Jackson) Thompson",
title = "Atlas for computing mathematical functions: an
illustrated guide for practitioners with programs in
{Fortran 90} and {Mathematica}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 888",
year = "1997",
ISBN = "0-471-18171-4 (cloth)",
ISBN-13 = "978-0-471-18171-2 (cloth)",
LCCN = "QA331.T386 1997",
bibdate = "Fri May 21 07:11:19 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Includes CD-ROM.",
acknowledgement = ack-nhfb,
annote = "A Wiley-Interscience publication. System requirements
for accompanying computer disc: Windows; Macintosh
compatible.",
keywords = "FORTRAN (Computer program language); Functions --
Computer programs; Mathematica (Computer program
language); Science -- Mathematics -- Computer
programs",
}
@Book{Yoshida:1997:HFM,
author = "Masaaki Yoshida",
title = "Hypergeometric functions, my love: modular
interpretations of configuration spaces",
volume = "E 32",
publisher = pub-VIEWEG,
address = pub-VIEWEG:adr,
pages = "xvi + 292",
year = "1997",
ISBN = "3-528-06925-2",
ISBN-13 = "978-3-528-06925-4",
ISSN = "0179-2156",
LCCN = "QA353.H9 Y67 1997",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Aspects of mathematics",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Configuration space",
}
@Article{Yousif:1997:BFF,
author = "Hashim A. Yousif and Richard Melka",
title = "{Bessel} function of the first kind with complex
argument",
journal = j-COMP-PHYS-COMM,
volume = "106",
number = "3",
pages = "199--206",
month = nov,
year = "1997",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(97)00087-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:21 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465597000878",
abstract = "A new method of computing integral order Bessel
functions of the first kind $J_n(z)$ when either the
absolute value of the real part or the imaginary part
of the argument $z = x + iy$ is small, is described.
This method is based on computing the Bessel functions
from asymptotic expressions when $x \sim 0$ (or $y \sim
0$). These expansions are derived from the integral
definition of Bessel functions. This method is
necessary because some existing algorithms and methods
fail to give correct results for small $x$ or small
$y$. In addition, our overall method of computing
Bessel functions of any order and argument is discussed
and the logarithmic derivative is used in computing
these functions. The starting point of the backward
recurrence relations needed to evaluate the Bessel
function and their logarithmic derivatives are
investigated in order to obtain accurate numerical
results. Our numerical method, together with
established techniques of computing the Bessel
functions, is easy to implement, efficient, and
produces reliable results for all $z$.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Aberbour:1998:PMF,
author = "M. Aberbour and A. Houelle and H. Mehrez and N.
Vaucher and A. Guyot",
title = "On portable macrocell {FPU} generators for division
and square root operators complying to the full
{IEEE-754} standard",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "6",
number = "1",
pages = "114--121",
month = mar,
year = "1998",
CODEN = "????",
DOI = "http://dx.doi.org/10.1109/92.661253",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "In this paper, we investigate the design of macrocell
generators of division and square root floating-point
operators. The number representation used in our
operators is the IEEE-754-1985 standard for binary
floating-point numbers. The design and \ldots{}",
}
@Book{Andrews:1998:SFM,
author = "Larry C. Andrews",
title = "Special functions of mathematics for engineers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Second",
pages = "xvii + 479",
year = "1998",
ISBN = "0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE
Press hardcover)",
ISBN-13 = "978-0-19-856558-1 (Oxford hardcover),
978-0-8194-2616-1 (SPIE Press)",
LCCN = "QA351 .A75 1998",
bibdate = "Sat Oct 30 16:44:00 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
library.ox.ac.uk:210/ADVANCE;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Originally published: New York : McGraw-Hill, c1992.",
subject = "Functions, Special",
tableofcontents = "Preface to the Second Edition \\
Preface to the First Edition \\
Notation for Special Functions \\
Infinite Series, Improper Integrals, and Infinite
Products \\
The Gamma Function and Related Functions \\
Other Functions Defined by Integrals \\
Legendre Polynomials and Related Functions \\
Other Orthogonal Polynomials \\
Bessel Functions \\
Bessel Functions of Other Kinds \\
Applications Involving Bessel Functions \\
The Hypergeometric Function \\
The Confluent Hypergeometric Functions \\
Generalized Hypergeometric Functions \\
Applications Involving Hypergeometric-Type Functions
\\
Bibliography \\
Appendix: A List of Special Function Formulas \\
Selected Answers to Exercises \\
Index",
}
@Book{Anonymous:1998:AMS,
editor = "Anonymous",
title = "Analytical methods and special functions",
publisher = "Gordon and Breach Science Publishers",
address = "Amsterdam, The Netherlands",
pages = "????",
year = "1998",
ISSN = "1027-0264",
LCCN = "A299.6 A533 v. 1 1998",
bibdate = "Sat Oct 30 19:02:18 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Antelo:1998:CVH,
author = "E. Antelo and T. Lang and J. D. Bruguera",
title = "Computation of $\sqrt{(x /d)}$ in a very high radix
combined division\slash square-root unit with scaling
and selection by rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "2",
pages = "152--161",
month = feb,
year = "1998",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.663761",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:53 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
summary = "A very-high radix digit-recurrence algorithm for the
operation {\surd}(x/d) is developed, with residual
scaling and digit selection by rounding. This is an
extension of the division and square-root algorithms
presented previously, and for which a \ldots{}",
}
@Article{BenGhanem:1998:QFU,
author = "Riadh {Ben Ghanem}",
title = "Quadrature formulae using zeros of {Bessel} functions
as nodes",
journal = j-MATH-COMPUT,
volume = "67",
number = "221",
pages = "323--336",
month = jan,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65D32",
MRnumber = "98c:65031",
MRreviewer = "Kai Diethelm",
bibdate = "Fri Jul 16 10:38:50 MDT 1999",
bibsource = "http://www.ams.org/mcom/1998-67-221;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
acknowledgement = ack-nhfb,
}
@TechReport{Borwein:1998:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
type = "Report",
number = "CECM-98-118",
institution = "Center for Experimental and Constructive Mathematics,
Simon Fraser University",
address = "Burnaby, BC, USA",
pages = "68",
day = "30",
month = oct,
year = "1998",
bibdate = "Mon Oct 24 11:29:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
acknowledgement = ack-nhfb,
}
@InCollection{Buhring:1998:ACG,
author = "Wolfgang B{\"u}hring and H. M. Srivastava",
editor = "Themistocles M. Rassias",
booktitle = "Approximation theory and applications",
title = "Analytic Continuation of the Generalized
Hypergeometric Series Near Unit Argument with Emphasis
on the Zero-Balanced Series",
publisher = "Hadronic Press",
address = "Palm Harbor, FL, USA",
pages = "17--35",
year = "1998",
ISBN = "1-57485-041-5",
ISBN-13 = "978-1-57485-041-3",
LCCN = "QA297.5 .A685 1998",
MRclass = "33C20; 41-06 (00B15)",
MRnumber = "MR1924838 (2003i:33006); MR1924835 (2003c:41003)",
bibdate = "Thu Dec 01 10:08:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/42786578.html",
acknowledgement = ack-nhfb,
bookpages = "v + 193",
remark = "The paper treats $_{p + 1}F_p(z)$ for $z \approx 1$.
Available as arxiv:math/0102032.",
}
@Article{Carsky:1998:IGF,
author = "Petr C{\'a}rsky and Martin Pol{\'a}sek",
title = "Incomplete Gamma {$F_m(x)$} Functions for Real
Negative and Complex Arguments",
journal = j-J-COMPUT-PHYS,
volume = "143",
number = "1",
pages = "259--265",
day = "10",
month = jun,
year = "1998",
CODEN = "JCTPAH",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999198959757",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Cornea-Hasegan:1998:PIC,
author = "Marius Cornea-Hasegan",
title = "Proving the {IEEE} Correctness of Iterative
Floating-Point Square Root, Divide, and Remainder
Algorithms",
journal = j-INTEL-TECH-J,
volume = "Q2",
number = "Q2",
pages = "11",
year = "1998",
ISSN = "1535-766X",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
acknowledgement = ack-nhfb,
}
@Article{Crenshaw:1998:ISR,
author = "Jack W. Crenshaw",
title = "Integer Square Roots",
journal = j-EMBED-SYS-PROG,
volume = "11",
number = "2",
pages = "15--32",
month = feb,
year = "1998",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Fri Nov 28 16:31:58 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.embedded.com/98/9802fe2.htm",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Deleglise:1998:C,
author = "Marc Del{\'e}glise and Jo{\"e}l Rivat",
title = "Computing $\psi(x)$",
journal = j-MATH-COMPUT,
volume = "67",
number = "224",
pages = "1691--1696",
month = oct,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "11Y35 (11N56)",
MRnumber = "1 474 649",
bibdate = "Fri Jul 16 10:38:58 MDT 1999",
bibsource = "http://www.ams.org/mcom/1998-67-224;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
acknowledgement = ack-nhfb,
}
@Article{Homeier:1998:AHC,
author = "Herbert H. H. Homeier",
title = "An asymptotically hierarchy-consistent, iterative
sequence transformation for convergence acceleration of
{Fourier} series",
journal = j-NUMER-ALGORITHMS,
volume = "18",
number = "1",
pages = "1--30",
month = sep,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Mon Sep 29 08:36:54 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf;
http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
tech = "Technical Report TC-NA-97-2, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
ZMnumber = "914.65140",
}
@Article{Homeier:1998:CAM,
author = "H. H. H. Homeier",
title = "On Convergence Acceleration of Multipolar and
Orthogonal Expansions",
journal = j-INTERNET-J-CHEM,
volume = "1",
number = "Article 28",
pages = "????",
year = "1998",
CODEN = "IJCHFJ",
ISSN = "1099-8292",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the {4$^{th}$ Electronic Computational
Chemistry Conference}.",
URL = "http://www.ijc.com/articles/1998v1/28/",
fjournal = "Internet Journal of Chemistry",
keywords = "convergence acceleration",
tech = "Technical Report TC-QM-97-5, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}
@Article{Kiranon:1998:SRV,
author = "W. Kiranon and N. Kumprasert",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G - Circuits, Devices and
Systems]",
volume = "145",
number = "2",
pages = "139",
month = apr,
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Recently, Lui [1995] presented a square-rooting
circuit using CCII, MOS transistors and a buffered
unity-gain inverting amplifier. It is interesting since
it finds various applications as described in his
paper. However, an error occurred in the \ldots{}",
}
@Article{Kramer:1998:PWC,
author = "W. Kramer",
title = "A priori worst case error bounds for floating-point
computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "750--756",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.709374",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Tang:1992:TDI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
abstract = "A new technique for the a priori calculation of
rigorous error bounds for floating-point computations
is introduced. The theorems given in the paper combined
with interval arithmetic lead to the implementation of
reliable software routines, which enable the user to
compute the desired error bounds automatically by a
suitable computer program. As a prominent example, a
table-lookup algorithm for calculating the function
$exp(x) - 1$ that has been published by P. T. P. Tang
(1992) is analyzed using these new tools. The result
shows the high quality of the new approach",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Kravanja:1998:ZMS,
author = "P. Kravanja and O. Ragos and M. N. Vrahatis and F. A.
Zafiropoulos",
title = "{ZEBEC}: a mathematical software package for computing
simple zeros of {Bessel} functions of real order and
complex argument",
journal = j-COMP-PHYS-COMM,
volume = "113",
number = "2--3",
pages = "220--238",
month = oct,
year = "1998",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:30 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598000642",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@InProceedings{Kuhlmann:1998:FLP,
author = "M. Kuhlmann and K. K. Parhi",
booktitle = "{Proceedings of the 1998 International Conference on
Computer Design: VLSI in Computers and Processors. ICCD
'98}",
title = "Fast low-power shared division and square-root
architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "128--135",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper addresses a fast low-power implementation
of a shared division and square-root architecture. Two
approaches are considered in this paper; these include
the SRT (Sweeney, Robertson and Tocher) approach which
does not require prescaling and \ldots{}",
}
@Article{Lefevre:1998:TCR,
author = "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
title = "Toward correctly rounded transcendentals",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1235--1243",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.736435",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The Table Maker's Dilemma is the problem of always
getting correctly rounded results when computing the
elementary functions. After a brief presentation of
this problem, we present new developments that have
helped us to solve this problem for the \ldots{}",
}
@Article{Morozov:1998:NWR,
author = "D. Kh. Morozov and V. V. Voitsekhovich",
title = "A new wide-range approximation of modified {Bessel}
functions in terms of elementary functions",
journal = "Rev. Mexicana F\'\i s.",
volume = "44",
number = "3",
pages = "231--234",
year = "1998",
CODEN = "RMXFAT",
ISSN = "0035-001X",
MRclass = "65D20",
MRnumber = "MR1629601",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Revista Mexicana de F\'\i sica",
}
@Article{Nguyen:1998:MLS,
author = "Phong Nguyen",
title = "A {Montgomery}-Like Square Root for the Number Field
Sieve",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1423",
pages = "151--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
bibdate = "Tue Feb 5 11:52:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
acknowledgement = ack-nhfb,
}
@Article{Qiu:1998:SIG,
author = "S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen",
title = "Some Inequalities for the Growth of Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "29",
number = "5",
pages = "1224--1237",
month = sep,
year = "1998",
CODEN = "SJMAAH",
DOI = "http://dx.doi.org/10.1137/S0036141096310491",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sat Dec 5 14:39:16 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31049",
acknowledgement = ack-nhfb,
}
@Article{Rivolo:1998:CDR,
author = "M. T. Rivolo and A. Simi",
title = "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
calculation of square and cube roots in {Italy} from
{Fibonacci} to {Bombelli}]",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "52",
number = "2",
pages = "161--193",
month = feb,
year = "1998",
CODEN = "AHESAN",
DOI = "http://dx.doi.org/10.1007/s004070050015",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A35 (01A40)",
MRnumber = "1610136 (99d:01015)",
MRreviewer = "Massimo Galuzzi",
bibdate = "Fri Feb 4 21:50:33 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
http://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
language = "Italian",
MRtitle = "The computation of square and cube roots in {Italy}
from {Fibonacci} to {Bombelli}",
}
@Article{Russinoff:1998:MCP,
author = "David M. Russinoff",
title = "A Mechanically Checked Proof of {IEEE} Compliance of
the Floating Point Multiplication, Division and Square
Root Algorithms of the {AMD-K7} Processor",
journal = j-LMS-J-COMPUT-MATH,
volume = "1",
pages = "148--200",
year = "1998",
CODEN = "????",
DOI = "http://dx.doi.org/10.1112/S1461157000000176",
ISSN = "1461-1570",
MRclass = "68M07 (65Y99 68T15)",
MRnumber = "99m:68015",
MRreviewer = "J. Michel Muller",
bibdate = "Fri Nov 29 08:13:48 2002",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=JCM;
http://www.math.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Appendices A and B available to subscribers
electronically
(http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
URL = "http://www.lms.ac.uk/jcm/1/lms1998-001/",
acknowledgement = ack-nhfb,
ajournal = "LMS J. Comput. Math.",
fjournal = "LMS Journal of Computation and Mathematics",
onlinedate = "01 February 2010",
}
@Article{Segura:1998:PCF,
author = "J. Segura and A. Gil",
title = "Parabolic cylinder functions of integer and
half-integer orders for nonnegative arguments",
journal = j-COMP-PHYS-COMM,
volume = "115",
number = "1",
pages = "69--86",
day = "1",
month = dec,
year = "1998",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:32 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598000976",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Sidi:1998:UBC,
author = "Avram Sidi and Yair Shapira",
title = "Upper bounds for convergence rates of acceleration
methods with initial iterations",
journal = j-NUMER-ALGORITHMS,
volume = "18",
number = "2",
pages = "113--132",
month = sep,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Mon Sep 29 08:36:55 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Agarwal:1999:SAM,
author = "R. C. Agarwal and F. G. Gustavson and M. S.
Schmookler",
title = "Series approximation methods for divide and square
root in the {Power3{\TM}} processor",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "116--123",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
http://euler.ecs.umass.edu/paper/final/paper-144.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "The Power3 processor is a 64-bit implementation of the
PowerPC TM architecture and is the successor to the
Power2 TM processor for workstations and servers which
REQUIRE high performance floating point capability. The
previous \ldots{}",
}
@Book{Andrews:1999:SF,
author = "George E. Andrews and Richard Askey and Ranjan Roy",
title = "Special Functions",
volume = "71",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 664",
year = "1999",
ISBN = "0-521-62321-9 (hardcover), 0-521-78988-5 (paperback)",
ISBN-13 = "978-0-521-62321-6 (hardcover), 978-0-521-78988-2
(paperback)",
LCCN = "QA351 .A74 1999",
bibdate = "Mon Sep 17 18:52:30 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90.00 (hardcover), US\$34.95 (paperback)",
series = "Encyclopedia of mathematics and its applications",
acknowledgement = ack-nhfb,
subject = "Functions, Special",
xxURL = "http://www.loc.gov/catdir/toc/cam024/98025757.html;
http://www.loc.gov/catdir/description/cam029/98025757.html",
}
@Article{Bach:1999:NTS,
author = "E. Bach and K. Huber",
title = "Note on taking square-roots modulo {$N$}",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "45",
number = "2",
pages = "807--809",
month = mar,
year = "1999",
CODEN = "IETTAW",
DOI = "http://dx.doi.org/10.1109/18.749034",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "In this article it is shown how Gauss' (1981) famous
cyclotomic sum formula can be used for extracting
square-roots modulo \ldots{}",
}
@InProceedings{Batten:1999:IBO,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and R. Peri and P. D'arcy",
editor = "????",
booktitle = "Proceedings of the International Conference on Signal
Processing Applications and Technologies, Orlando,
Florida, November, 1999",
title = "Interactions Between Optimizations and a New Type of
{DSP} Intrinsic Function",
publisher = "????",
address = "????",
year = "1999",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 11:05:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Shortened version in \cite{Batten:1999:IFB}.",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
acknowledgement = ack-nhfb,
}
@Article{Batten:1999:IFB,
author = "D. Batten and P. D'arcy",
title = "Intrinsic Functions Boost Compilers",
journal = "Electrical Engineering Times",
volume = "1085",
pages = "104--104",
month = nov,
year = "1999",
bibdate = "Sun Mar 04 11:06:22 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Brezinski:1999:EEC,
author = "C. Brezinski",
booktitle = "Error control and adaptivity in scientific computing
({Antalya}, 1998)",
title = "Error estimates and convergence acceleration",
volume = "536",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "87--94",
year = "1999",
MRclass = "65B05 (65D15)",
MRnumber = "1735125",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "NATO Sci. Ser. C Math. Phys. Sci.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Bui:1999:DSI,
author = "H. Bui and S. Tahar",
booktitle = "1999 IEEE Canadian Conference on Electrical and
Computer Engineering, 9--12 May 1999",
title = "Design and synthesis of an {IEEE-754} exponential
function",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "450--455",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We have designed a floating-point exponential function
using the table-driven method. The algorithm was first
implemented using sequential VHDL and later translated
to Concurrent Verilog. The main part of the work
consisted of creating modules that \ldots{}",
}
@Article{Cappuccino:1999:HSS,
author = "G. Cappuccino and G. Cocorullo and P. Corsonello and
S. Perri",
title = "High speed self-timed pipelined datapath for square
rooting",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G --- Circuits, Devices and
Systems]",
volume = "146",
number = "1",
pages = "16--22",
month = feb,
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The authors describe a new high-performance self-timed
circuit for asynchronous square rooting. The new
architecture is based on a modified nonrestoring
algorithm. An asynchronous pipelined cellular array
without auxiliary system for the \ldots{}",
}
@Article{Carlson:1999:TSI,
author = "B. C. Carlson",
title = "Toward Symbolic Integration of Elliptic Integrals",
journal = j-J-SYMBOLIC-COMP,
volume = "28",
number = "6",
pages = "739--753",
month = dec,
year = "1999",
CODEN = "JSYCEH",
DOI = "http://dx.doi.org/10.1006/jsco.1999.0336",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
bibdate = "Tue Mar 7 11:48:04 MST 2000",
bibsource = "http://www.idealibrary.com/cgi-bin/links/toc/sy;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref",
acknowledgement = ack-nhfb,
}
@InProceedings{Cornea-Hasegan:1999:CPO,
author = "M. A. Cornea-Hasegan and R. A. Golliver and P.
Markstein",
title = "Correctness proofs outline for {Newton--Raphson} based
floating-point divide and square root algorithms",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "96--105",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
http://euler.ecs.umass.edu/paper/final/paper-121.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "This paper describes a study of a class of algorithms
for the floating-point divide and square root
operations, based on the Newton--Raphson iterative
method. The two main goals were. (1) Proving the IEEE
correctness of these iterative floating-point
\ldots{}",
}
@Article{Corsonello:1999:HPS,
author = "P. Corsonello and S. Perri",
title = "High performance square rooting circuit using hybrid
radix-$2$ adders",
journal = j-ELECT-LETTERS,
volume = "35",
number = "3",
pages = "185--186",
day = "4",
month = feb,
year = "1999",
CODEN = "ELLEAK",
ISSN = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A new high performance bit parallel architecture for
computing square roots is proposed. The architecture
implements a non-restoring algorithm and is structured
as a pipelined cellular array. To improve the
performance, hybrid radix-$2$ adders are \ldots{}",
}
@Article{Elbert:1999:SFZ,
author = "{\'A}rp{\'a}d Elbert and Panayiotis D. Siafarikas",
title = "On the Square of the First Zero of the {Bessel}
Function {$J_\nu(z)$}",
journal = j-CAN-MATH-BULL,
volume = "42",
number = "1",
pages = "56--77",
month = mar,
year = "1999",
CODEN = "CMBUA3",
DOI = "http://dx.doi.org/10.4153/CMB-1999-007-4",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "33A40",
bibdate = "Thu Sep 8 10:22:25 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v42/;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Let $j_{\nu,1}$ be the smallest (first) positive zero
of the Bessel function $J_{\nu}(z)$, $\nu>-1$, which
becomes zero when $\nu$ approaches $-1$. Then
$j_{\nu,1}^2$ can be continued analytically to
$-2<\nu<-1$, where it takes on negative values. We show
that $j_{\nu,1}^2$ is a convex function of $\nu$ in the
interval $-2<\nu\leq 0$, as an addition to an old
result [{\'A}. Elbert and A. Laforgia, SIAM J. Math.
Anal. {\bf 15}(1984), 206--212], stating this convexity
for $\nu>0$. Also the monotonicity properties of the
functions $\frac{j_{\nu,1}^2}{4 (\nu+1)}$,
$\frac{j_{\nu,1}^2}{4(\nu+1)\sqrt{\nu+2}}$ are
determined. Our approach is based on the series
expansion of Bessel function $J_{\nu}(z)$ and it turned
out to be effective, especially when $-2<\nu<-1$.",
acknowledgement = ack-nhfb,
ams-subject-primary = "33A40",
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journalabbrev = "CMB",
refnum = "7139",
xxpages = "56--67",
}
@Article{Gautschi:1999:NRC,
author = "Walter Gautschi",
title = "A Note on the Recursive Calculation of Incomplete
Gamma Functions",
journal = j-TOMS,
volume = "25",
number = "1",
pages = "101--107",
month = mar,
year = "1999",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Thu Jul 15 19:01:02 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/305658.305717;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC;
http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/",
abstract = "It is known that the recurrence relation for
incomplete gamma functions $\Gamma(a + n, x), 0 \le a <
1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is
unstable---more so the larger $x$. Nevertheless, the
recursion can be used in the range $0 \le n \le x$
practically without error growth, and in larger ranges
$0 \le n \le N$ with a loss of accuracy that can be
controlled by suitably limiting $N$.",
acknowledgement = ack-nhfb,
keywords = "algorithms; reliability",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Stability (and instability). {\bf
G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation.",
}
@TechReport{Gourdon:1999:NCC,
author = "Xavier Gourdon and Pascal Sebah",
title = "Numbers, constants, and computation",
institution = "????",
address = "Paris, France",
year = "1999",
bibdate = "Sat Mar 15 16:28:07 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "World-Wide Web site.",
URL = "http://numbers.computation.free.fr/Constants/home.html",
acknowledgement = ack-nhfb,
annote = "Although this site concentrates mainly on computation
of particular mathematical constants, it also treats
high-precision computation of inverse and square
root.",
}
@Article{Harrison:1999:CTF,
author = "John Harrison and Ted Kubaska and Shane Story and Ping
Tak Peter Tang",
title = "The Computation of Transcendental Functions on the
{IA-64} Architecture",
journal = j-INTEL-TECH-J,
number = "Q4",
pages = "7",
day = "22",
month = nov,
year = "1999",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
acknowledgement = ack-nhfb,
}
@Article{Homeier:1999:CAL,
author = "H. H. H. Homeier",
title = "Convergence acceleration of logarithmically convergent
series avoiding summation",
journal = j-APPL-MATH-LETT,
volume = "12",
number = "3",
pages = "29--32",
year = "1999",
CODEN = "AMLEEL",
DOI = "http://dx.doi.org/10.1016/S0893-9659(98)00167-0",
ISSN = "0893-9659",
ISSN-L = "0893-9659",
MRclass = "65B05",
MRnumber = "1749733",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
keywords = "convergence acceleration",
}
@InProceedings{Hyogo:1999:LVF,
author = "A. Hyogo and Y. Fukutomi and K. Sekine",
booktitle = "Proceedings of the 1999 IEEE International Symposium
on Circuits and Systems: ISCAS '99, 2 June 1999",
title = "Low voltage four-quadrant analog multiplier using
square-root circuit based on {CMOS} pair",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "274--277",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We proposed a square-root circuit based on CMOS pairs.
In this paper, we propose a low voltage four-quadrant
analog multiplier using the square-root circuit. Also
we confirmed this operation by PSpice \ldots{}",
}
@Article{Iordache:1999:ARS,
author = "Cristina Iordache and David W. Matula",
title = "Analysis of Reciprocal and Square Root Reciprocal
Instructions in the {AMD K6-2} Implementation of
{3DNow!}",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "24",
pages = "34--62",
year = "1999",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S1571-0661(05)80621-8",
ISSN = "1571-0661",
bibdate = "Fri Jun 24 20:23:13 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Reciprocal and root reciprocal functions at ``half''
and IEEE single precision formats are specified in the
AMD 3DNow! instruction set. Implementations in the
recently released AMD K6-2 microprocessor are analyzed
herein by exhaustive computation and timing loops to
ascertain the accuracy and monotonicity properties of
the output and throughput\slash latency cycle counts.
Periodicities in stepwise function output were observed
and employed to construct an underlying bipartite table
that can serve as the core of the respective reciprocal
function outputs. The recommended RISC instruction
macros generated single precision reciprocals and root
reciprocals accurate to a unit in the last place.
However, the root reciprocal functions failed to
satisfy the desirable monotonicity property typically
implemented as an industry standard for elementary
functions on x86 floating point units. Reasons for the
failure are provided and an adjusted table is shown to
satisfy the monotonicity standard. Results are
summarized in Table 1 and described in the body of this
report.",
acknowledgement = ack-nhfb,
}
@InProceedings{Iordache:1999:IPR,
author = "Cristina Iordache and David W. Matula",
title = "On Infinitely Precise Rounding for Division, Square
Root, Reciprocal and Square Root Reciprocal",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--240",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
http://euler.ecs.umass.edu/paper/final/paper-164.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
abstract = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds on the number of
bits of an approximation accurate to a unit in the last
place sufficient to guarantee that correct round and
sticky bits can be determined. Known lower bounds for
quotients and square roots are given and/or sharpened,
and a new lower bound for root reciprocals is proved.
Specifically for reciprocals, quotients and square
roots, tight bounds of order $2p + O(1)$ are presented.
For infinitely precise rounding of the root reciprocal
a lower bound can be found at $3p + O(1)$, but
exhaustive testing for small sizes of the operand
suggests that in practice $(2+\epsilon)p$ for small
$\epsilon$ is usually sufficient. Algorithms can be
designed for obtaining the round and sticky bits based
on the bit pattern of an approximation computed to the
required accuracy. We show that some improvement of the
known lower bound for reciprocals and division is
achievable at the cost of somewhat more complex
hardware for rounding. Tests for the exactness of the
quotient and square root are also provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; IEEE",
summary = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds \ldots{}",
}
@Article{Jamieson:1999:NRF,
author = "M. J. Jamieson",
title = "Notes: On rational function approximations to square
roots",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "1",
pages = "50--52",
month = jan,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Yxx",
MRnumber = "1 674 202",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1999:SRD,
author = "W. Kahan",
title = "Square Root Without Division",
howpublished = "World-Wide Web document",
pages = "3",
day = "23",
month = feb,
year = "1999",
bibdate = "Mon Apr 25 18:01:49 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
acknowledgement = ack-nhfb,
}
@Article{Krukier:1999:CAT,
author = "L. A. Krukier",
title = "Convergence acceleration of triangular iterative
methods based on the skew-symmetric part of the
matrix",
journal = j-APPL-NUM-MATH,
volume = "30",
number = "2--3",
pages = "281--290",
day = "10",
month = jun,
year = "1999",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
bibdate = "Wed Jul 28 14:37:31 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Kzaz:1999:CAG,
author = "M. Kzaz",
title = "Convergence acceleration of the {Gauss--Laguerre}
quadrature formula",
journal = j-APPL-NUM-MATH,
volume = "29",
number = "2",
pages = "201--220",
day = "1",
month = feb,
year = "1999",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
bibdate = "Wed Jul 28 14:37:22 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Lang:1999:VHR,
author = "T. Lang and P. Montuschi",
title = "Very high radix square root with prescaling and
rounding and a combined division\slash square root
unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "827--841",
month = aug,
year = "1999",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.795124",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root with prescaling and
selection by rounding is developed and combined with a
similar scheme for division. Since division is usually
more frequent than square root, the main concern of the
combined implementation is to \ldots{}",
}
@InProceedings{Lee:1999:STS,
author = "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
Seung-Ho Hwang",
booktitle = "6th International Conference on VLSI and CAD: ICVC
'99",
title = "Self-timed shared division and square-root
implementation using full redundant signed digit
numbers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "541--544",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A radix-$2$ square root implementation for self-timed
dividers using redundant signed-digit (RSD) adders is
presented. In this method, two self-timed RSD adder
stages are used for each result bit selection. A very
efficient and simple result bit \ldots{}",
}
@InProceedings{Lozier:1999:DDM,
author = "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
title = "Design of a Digital Mathematical Library for Science,
Technology and Education",
crossref = "IEEE:1999:PIF",
pages = "118--128",
year = "1999",
bibdate = "Fri Jul 09 06:33:35 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
acknowledgement = ack-nhfb,
remark = "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}
@Article{Morita:1999:CEI,
author = "T. Morita",
title = "Calculation of the elliptic integrals of the first and
second kinds with complex modulus",
journal = j-NUM-MATH,
volume = "82",
number = "4",
pages = "677--688",
month = jun,
year = "1999",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 10:45:11 MDT 1999",
bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm;
http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf",
acknowledgement = ack-nhfb,
}
@Article{Muller:1999:CAT,
author = "J. M{\"u}ller",
title = "Convergence acceleration of {Taylor} sections by
convolution",
journal = j-CONST-APPROX,
volume = "15",
number = "4",
pages = "523--536",
year = "1999",
DOI = "http://dx.doi.org/10.1007/s003659900120",
ISSN = "0176-4276",
ISSN-L = "0176-4276",
MRclass = "41A58 (30E10)",
MRnumber = "1702803 (2000i:41040)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Constructive Approximation",
keywords = "convergence acceleration",
}
@InProceedings{Nannarelli:1999:LPR,
author = "A. Nannarelli and T. Lang",
booktitle = "(ICCD '99) International Conference on Computer
Design",
title = "Low-power radix-$4$ combined division and square
root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "236--242",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Because of the similarities in the algorithm it is
quite common to implement division and square root in
the same unit. The purpose of this work is to implement
a low-power combined radix-$4$ division and square root
floating-point double precision \ldots{}",
}
@InProceedings{Oberman:1999:FPD,
author = "S. F. Oberman",
title = "Floating point division and square root algorithms and
implementation in the {AMD-K7{\TM}} microprocessor",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "106--115",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
http://euler.ecs.umass.edu/paper/final/paper-139.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "This paper presents the AMD-K7 IEEE 754 and $\times$87
compliant floating point division and square root
algorithms and implementation. The AMD-K7 processor
employs an iterative implementation of a series
expansion to converge quadratically to the \ldots{}",
}
@InProceedings{Parhami:1999:ALT,
author = "B. Parhami",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Analysis of the lookup table size for square-rooting",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1327--1330",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Convergence methods are widely used for division,
reciprocation, and square-rooting. With such methods,
it is common to use an initial table lookup step for
obtaining an approximate result that leads to faster
convergence. In the case of division \ldots{}",
}
@Article{Russinoff:1999:MCP,
author = "David M. Russinoff",
title = "A mechanically checked proof of correctness of the
{AMD K5} floating point square root microcode",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "75--125",
month = jan,
year = "1999",
CODEN = "FMSDE6",
ISSN = "0925-9856",
bibdate = "Sat Jun 02 07:51:51 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special issue on arithmetic circuits.",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194808",
acknowledgement = ack-nhfb,
}
@Article{Schraudolph:1999:FCA,
author = "N. N. Schraudolph",
title = "A Fast, Compact Approximation of the Exponential
Function",
journal = j-NEURAL-COMP,
volume = "11",
number = "4",
pages = "853--862",
day = "1",
month = may,
year = "1999",
CODEN = "NEUCEB",
ISSN = "0899-7667",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "10",
}
@Article{Schulte:1999:AEF,
author = "M. Schulte and J. Stine",
title = "Approximating Elementary Functions with Symmetric
Bipartite Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "842--847",
year = "1999",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.795125",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:20:58 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1999:ESO,
author = "M. J. Schulte and K. E. Wires",
title = "Efficient Second Order Approximations for Reciprocals
and Square Roots",
crossref = "Luk:1999:PSA",
volume = "3807",
pages = "10--18",
year = "1999",
bibdate = "Sun Mar 04 11:10:48 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1999:HSI,
author = "Michael J. Schulte and Kent E. Wires",
title = "High-Speed Inverse Square Roots",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "124--131",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
http://euler.ecs.umass.edu/paper/final/paper-109.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "Inverse square roots are used in several digital
signal processing, multimedia, and scientific computing
applications. This paper presents a high-speed method
for computing inverse square roots. This method uses a
table lookup, operand modification, \ldots{}",
}
@Article{Segura:1999:EGT,
author = "J. Segura and A. Gil",
title = "{ELF} and {GNOME}: Two tiny codes to evaluate the real
zeros of the {Bessel} functions of the first kind for
real orders",
journal = j-COMP-PHYS-COMM,
volume = "117",
number = "3",
pages = "250--262",
day = "11",
month = mar,
year = "1999",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:36 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598001933",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Seidel:1999:HSR,
author = "P.-M. Seidel",
title = "High-speed redundant reciprocal approximation",
journal = j-INTEGRATION-VLSI-J,
volume = "28",
number = "1",
pages = "1--12",
month = sep,
year = "1999",
CODEN = "IVJODL",
ISSN = "0167-9260",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "12",
}
@Article{Stine:1999:STA,
author = "E. Stine and M. J. Schulte",
title = "The Symmetric Table Addition Method for Accurate
Function Approximation",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "21",
number = "2",
pages = "167--177",
month = jun,
year = "1999",
CODEN = "JVSPED",
ISSN = "0922-5773",
bibdate = "Sun Mar 04 11:02:59 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Story:1999:NAI,
author = "S. Story and P. T. P. Tang",
title = "New Algorithms for Improved Transcendental Functions
on {IA-64}",
crossref = "Koren:1999:ISC",
pages = "4--11",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
http://euler.ecs.umass.edu/paper/final/paper-118.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
}
@Book{Suetin:1999:OPT,
author = "P. K. (Pavel Kondratevich) Suetin",
title = "Orthogonal polynomials in two variables",
volume = "3",
publisher = "Gordon and Breach Science Publishers",
address = "Amsterdam, The Netherlands",
pages = "xx + 348",
year = "1999",
ISBN = "90-5699-167-1",
ISBN-13 = "978-90-5699-167-8",
LCCN = "QA404.5 .S8813 1999",
bibdate = "Sat Oct 30 17:21:54 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Translated from the Russian by E. V. Pankratiev.",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
remark = "Originally published in Russian in 1988 by Nauka,
Moscow.",
subject = "Orthogonal polynomials",
}
@Article{Vrahatis:1999:ESP,
author = "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
Zafiropoulos and T. N. Grapsa",
title = "Erratum to: {{\booktitle{RFSFNS: a portable package
for the numerical determination of the number and the
calculation of roots of Bessel functions}} [Comput.
Phys. Commun. {\bf 92} (1995) 252--266]}",
journal = j-COMP-PHYS-COMM,
volume = "117",
number = "3",
pages = "290--290",
day = "11",
month = mar,
year = "1999",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:36 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00104655",
note = "See \cite{Vrahatis:1995:RPP}.",
URL = "http://www.sciencedirect.com/science/article/pii/S001046559800109X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Article{Wieder:1999:ANH,
author = "Thomas Wieder",
title = "{Algorithm 794}: Numerical {Hankel} transform by the
{Fortran} program {HANKEL}",
journal = j-TOMS,
volume = "25",
number = "2",
pages = "240--250",
month = jun,
year = "1999",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/317275.317284;
http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
http://www.netlib.org/toms/794;
ftp://netlib.bell-labs.com/netlib/toms/794.gz;
http://www.netlib.no/netlib/toms/794;
http://www.hensa.ac.uk/netlib/toms/794.gz;
http://phase.etl.go.jp/netlib/toms/794",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Oct 20 18:21:35 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The numerical evaluation of the Hankel transform poses
the problems of both infinite integration and Bessel
function calculation. Using the corresponding numerical
program routines from the literature, a Fortran program
has been written to perform the Hankel transform for
real functions, given either in analytical form as
subroutines or in discrete form as tabulated data.",
accepted = "February 1999",
acknowledgement = ack-nhfb,
keywords = "Hankel transform; numerical analysis",
subject = "Software --- Programming Languages --- Language
Classifications (D.3.2): FORTRAN 77; Theory of
Computation --- Analysis of Algorithms and Problem
Complexity --- Numerical Algorithms and Problems
(F.2.1): Computation of transforms;",
}
@TechReport{Zimmermann:1999:KSR,
author = "Paul Zimmermann",
title = "{Karatsuba} Square Root",
type = "Research Report",
number = "3805",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "8",
year = "1999",
bibdate = "Sun Sep 10 08:56:48 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
http://www.inria.fr/rrrt/rr-3805.html",
abstract = "We exhibit an algorithm to compute the square-root
with remainder of a $n$-word number in $3/2$ word
operations, where $K(n)$ is the number of words
operations to multiply two $n$-word numbers using
Karatsuba's algorithm. If the remainder is not needed,
the cost can be reduced to $K(n)$ on average. This
algorithm can be used for floating-point or polynomial
computations too; although not optimal asymptotically,
its simplicity gives a wide range of use, from about 50
to 1,000,000 digits, as shown by computer
experiments.",
acknowledgement = ack-nhfb,
}
@Article{Alhargan:2000:ACA,
author = "Fayez A. Alhargan",
title = "Algorithms for the Computation of all {Mathieu}
Functions of Integer Orders",
journal = j-TOMS,
volume = "26",
number = "3",
pages = "390--407",
month = sep,
year = "2000",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/358407.358420",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The paper presents methods for the computation of all
Mathieu functions of integer order, which cover a large
range of $n$ and $h$; previous algorithms were limited
to small values of $n$. The algorithms are given in
sufficient details to enable straightforward
implementation. The algorithms can handle a large range
of the order $n$ (0-200) and the parameter $h$
(0-4$n$).",
accepted = "19 May 2000",
acknowledgement = ack-nhfb,
}
@Article{Alhargan:2000:ASC,
author = "Fayez A. Alhargan",
title = "{Algorithm 804}: subroutines for the computation of
{Mathieu} functions of integer orders",
journal = j-TOMS,
volume = "26",
number = "3",
pages = "408--414",
month = sep,
year = "2000",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/358407.358422",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Computer subroutines in C++ for computing Mathieu
functions of integer orders are described. The core
routines for computing Mathieu characteristic numbers
and Mathieu coefficients are described in details, the
rest of the subroutines are standard implementation of
the series summations for each function. The routines
can handle a large range of the order $n$ and the
parameter $h$.",
accepted = "19 May 2000",
acknowledgement = ack-nhfb,
}
@Article{Anderson:2000:RAF,
author = "Stuart Anderson",
title = "Remark on {Algorithm 723}: {Fresnel} integrals",
journal = j-TOMS,
volume = "26",
number = "4",
pages = "617--617",
month = dec,
year = "2000",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/365723.365737",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
accepted = "16 October 2000",
acknowledgement = ack-nhfb,
}
@InProceedings{Batten:2000:NAD,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and P. D'arcy",
title = "A New Approach to {DSP} Intrinsic Functions",
crossref = "Sprague:2000:PAH",
pages = "2892--2901",
year = "2000",
bibdate = "Sun Mar 04 11:18:38 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Becken:2000:ACG,
author = "W. Becken and P. Schmelcher",
title = "The analytic continuation of the {Gaussian}
hypergeometric function {$_2F_1(a; b; c; z)$} for
arbitrary parameters",
journal = j-J-COMP-APPL-MATH,
volume = "126",
number = "1--2",
pages = "449--478",
day = "30",
month = dec,
year = "2000",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/S0377-0427(00)00267-3",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33C05 (33F05)",
MRnumber = "MR1806771 (2002e:33003)",
bibdate = "Thu Dec 01 09:08:29 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
}
@Article{Borwein:2000:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
journal = j-J-COMP-APPL-MATH,
volume = "121",
number = "1--2",
pages = "247--296",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/S0377-0427(00)00336-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Mon Oct 24 11:41:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling''.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
}
@Book{Bressoud:2000:CCN,
author = "David M. Bressoud and S. Wagon",
title = "A course in computational number theory",
publisher = "Key College Publishers in cooperation with Springer",
address = "New York, NY, USA",
pages = "xii + 367",
year = "2000",
ISBN = "1-93019-010-7",
ISBN-13 = "978-1-93019-010-8",
LCCN = "QA241 .B788 2000",
bibdate = "Fri Sep 26 14:29:31 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
acknowledgement = ack-nhfb,
subject = "Number theory; Algorithms",
}
@Article{Brezinski:2000:CAD,
author = "C. Brezinski",
title = "Convergence acceleration during the 20th century",
journal = j-J-COMP-APPL-MATH,
volume = "122",
number = "1--2",
pages = "1--21",
month = oct,
year = "2000",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/S0377-0427(00)00360-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65-03 (01A60)",
MRnumber = "1794649",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Numerical analysis 2000, Vol. II: Interpolation and
extrapolation",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
keywords = "convergence acceleration",
}
@Article{Cawley:2000:FCA,
author = "G. C. Cawley",
title = "On a Fast, Compact Approximation of the Exponential
Function",
journal = j-NEURAL-COMP,
volume = "12",
number = "9",
pages = "2009--2012",
day = "1",
month = sep,
year = "2000",
CODEN = "NEUCEB",
ISSN = "0899-7667",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "4",
}
@Article{Cherri:2000:PCC,
author = "A. K. Cherri and M. S. Alam",
title = "Parallel computation of complex elementary functions
using quaternary signed-digit arithmetic",
journal = "Optics and Laser Technology",
volume = "32",
number = "6",
pages = "391--399",
year = "2000",
CODEN = "????",
ISSN = "0030-3992",
bibdate = "Sat Dec 7 09:21:28 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "9",
}
@InProceedings{Chu:2000:CPT,
author = "Wanming Chu and Yamin Li",
booktitle = "ACAC 2000: 5th Australasian Computer Architecture
Conference",
title = "Cost\slash performance tradeoff of $n$-select square
root implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "9--16",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Hardware square-root units require large numbers of
gates even for iterative implementations. In this paper
we present four low-cost high-performance
fully-pipelined n-select implementations (nS-Root)
based on a non-restoring-remainder square root
\ldots{}",
}
@Article{Cohen:2000:CAA,
author = "Henri Cohen and Fernando {Rodriguez Villegas} and Don
Zagier",
title = "Convergence Acceleration of Alternating Series",
journal = j-EXP-MATH,
volume = "9",
number = "1",
pages = "3--12",
year = "2000",
ISSN = "1058-6458",
ISSN-L = "1058-6458",
MRclass = "11Y55 (65B05)",
MRnumber = "1758796 (2001m:11222)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://projecteuclid.org/euclid.em/1046889587;
http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps",
abstract = "We discuss some linear acceleration methods for
alternating series which are in theory and in practice
much better than that of Euler--Van Wijngaarden. One of
the algorithms, for instance, allows one to calculate
$\sum(-1)^ka_k$ with an error of about $17.93^{-n}$
from the first $n$ terms for a wide class of sequences
$\{a_k\}$. Such methods are useful for high precision
calculations frequently appearing in number theory.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
keywords = "convergence acceleration",
ZMnumber = "0972.11115",
}
@Article{Ercegovac:2000:IGD,
author = "Milos D. Ercegovac and Laurent Imbert and David W.
Matula and Jean-Michel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "759--763",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.863046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "The aim of this paper is to accelerate division,
square root, and square root reciprocal computations
when the Goldschmidt method is used on a pipelined
multiplier. This is done by replacing the last
iteration by the addition of a correcting term
\ldots{}",
}
@Article{Ercegovac:2000:RSR,
author = "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
Muller and Arnaud Tisserand",
title = "Reciprocation, Square Root, Inverse Square Root, and
Some Elementary Functions Using Small Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "628--637",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.863031",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07 (65B15)",
MRnumber = "MR1783602 (2001e:68016)",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Institute of Electrical and Electronics Engineers.
Transactions on Computers",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "This paper deals with the computation of reciprocals,
square roots, inverse square roots, and some elementary
functions using small tables, small multipliers, and,
for some functions, a final ``large'' (almost
full-length) multiplication. \ldots{}",
}
@Article{Favati:2000:SAC,
author = "P. Favati and G. Lotti and O. Menchi and F. Romani",
title = "Separable asymptotic cost of evaluating elementary
functions",
journal = j-NUMER-ALGORITHMS,
volume = "24",
number = "3",
pages = "255--274",
year = "2000",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
MRclass = "65Y20",
MRnumber = "MR1780414 (2001d:65174)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
pagecount = "20",
}
@InProceedings{Hasan:2000:FPI,
author = "M. A. Hasan and A. A. Hasan and S. Rahman",
booktitle = "Proceedings of the 39th IEEE Conference on Decision
and Control",
title = "Fixed point iterations for computing square roots and
the matrix sign function of complex matrices",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "4253--4258",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this work has been the development of
new set of rational iterations for computing square
roots and the matrix sign function of complex matrices.
Given any positive integer r{\&}ges;2, we presented a
systematic way of deriving rth order \ldots{}",
}
@InProceedings{Hassibi:2000:ESR,
author = "B. Hassibi",
booktitle = "Proceedings. 2000 IEEE International Conference on
Acoustics, Speech, and Signal Processing: ICASSP '00,
5--9 June 2000",
title = "An efficient square-root algorithm for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II737--II740",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@InProceedings{Hassibi:2000:FSR,
author = "B. Hassibi",
booktitle = "{Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000}",
title = "A fast square-root implementation for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1255--1259",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@Article{Holmgren:2000:CAL,
author = "Sverker Holmgren and Henrik Brand{\'e}n and Erik
Sterner",
title = "Convergence Acceleration for the Linearized
{Navier--Stokes} Equations using Semicirculant
Approximations",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1524--1550",
month = jul,
year = "2000",
CODEN = "SJOCE3",
DOI = "http://dx.doi.org/10.1137/S1064827597317983",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31798",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Lefevre:2000:CRF,
author = "V. D. Lefevre and J.-M. Muller",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Correctly rounded functions for better arithmetic",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "875--878",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The IEEE 754 standard for floating-point arithmetic
requires that the four arithmetic operations and the
square root should be correctly rounded. This has
improved the accuracy, reliability and portability of
numerical software. Unfortunately, such \ldots{}",
}
@Article{Lopez:2000:AES,
author = "Jos{\'e} L. L{\'o}pez",
title = "Asymptotic Expansions of Symmetric Standard Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "31",
number = "4",
pages = "754--775",
year = "2000",
CODEN = "SJMAAH",
DOI = "http://dx.doi.org/10.1137/S0036141099351176",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Fri Oct 27 08:17:04 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35117",
acknowledgement = ack-nhfb,
}
@InProceedings{Lozier:2000:DPN,
author = "Daniel W. Lozier",
title = "The {DLMF Project}: {A} New Initiative in Classical
Special Functions",
crossref = "Dunkl:2000:PIW",
pages = "207--220",
year = "2000",
bibdate = "Fri Jul 09 06:31:32 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Markstein:2000:IEF,
author = "Peter Markstein",
title = "{IA-64} and elementary functions: speed and
precision",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xix + 298",
year = "2000",
ISBN = "0-13-018348-2",
ISBN-13 = "978-0-13-018348-4",
LCCN = "QA76.9.A73 M365 2000",
bibdate = "Fri Jan 5 08:00:52 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
University of California MELVYL catalog.",
series = "Hewlett--Packard professional books",
acknowledgement = ack-nhfb,
annote = "Besides recipes for accurate computation of elementary
functions, this book also contains algorithms for the
correctly-rounded computation of floating-point
division and square-root, and of integer division,
starting from low-precision reciprocal approximations.
There is also a wealth of information on the tradeoffs
between integer and floating-point instruction use in a
pipelined parallel architecture.",
keywords = "IA-64 (computer architecture)",
}
@Article{Paliouras:2000:FPP,
author = "V. Paliouras and K. Karagianni and T. Stouraitis",
title = "A floating-point processor for fast and accurate
sine\slash cosine evaluation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "47",
number = "5",
pages = "441--451",
month = may,
year = "2000",
CODEN = "ICSPE5",
DOI = "http://dx.doi.org/10.1109/82.842112",
ISSN = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A VLSI architecture for fast and accurate
floating-point sine/cosine evaluation is presented,
combining floating-point and simple fixed-point
arithmetic. The algorithm implemented by the
architecture is based on second order polynomial
interpolation \ldots{}",
}
@InProceedings{Takahashi:2000:IMP,
author = "D. Takahashi",
booktitle = "Proceedings of the 2000 International Workshops on
Parallel Processing",
title = "Implementation of multiple-precision parallel division
and square root on distributed-memory parallel
computers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--235",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present efficient parallel algorithms for
multiple-precision division and square root operation
of more than several million decimal digits on
distributed-memory parallel computers. It is well known
that multiple-precision division and square \ldots{}",
}
@InProceedings{Tchoumatchenko:2000:FBS,
author = "V. Tchoumatchenko and T. Vassileva and P. Gurov",
booktitle = "{Proceedings of the 22nd EUROMICRO Conference
EUROMICRO 96. 'Beyond 2000: Hardware and Software
Design Strategies'}",
title = "A {FPGA} based square-root coprocessor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "520--525",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present an FPGA implementation of a non-restoring
integer square-root algorithm, that uses estimates for
result-digit selection and radix-$2$ redundant addition
in recurrence. On-the-fly conversion of the
result-digit and signed-digit adder/ \ldots{}",
}
@InProceedings{Tommiska:2000:AEI,
author = "M. T. Tommiska",
booktitle = "Proceedings of the 2000 Third IEEE International
Caracas Conference on Devices, Circuits and Systems,
15--17 March 2000",
title = "Area-efficient implementation of a fast square root
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "S18/1--S18/4",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An area-efficient implementation of a fast-converging
square-root algorithm is presented. The design of
special arithmetic operations differs in many ways from
the traditional tasks that digital designers are used
to, and the role of \ldots{}",
}
@TechReport{Zimmermann:2000:PGF,
author = "Paul Zimmermann",
title = "A proof of {GMP} fast division and square root
implementations",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "14",
month = sep,
year = "2000",
bibdate = "Sun Sep 10 08:48:46 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
abstract = "This short note gives a detailed correctness proof of
fast (i.e., subquadratic) versions of the GNU MP {\tt
mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
together with complete GMP code. The {\tt
mpn\_bz\_divrem\_n} function divides (with remainder) a
number of $2n$ limbs by a divisor of $n$ limbs in
$2K(n)$, where $K(n)$ is the time spent in a $(n \times
n)$ multiplication, using the
Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
The {\tt mpn\_sqrtrem} computes the square root and the
remainder of a number of $2n$ limbs (square root and
remainder have about $n$ limbs each) in time $3K(n)/2$;
it uses Karatsuba Square Root.",
acknowledgement = ack-nhfb,
}
@Book{Askey:2001:SFG,
editor = "R. A. Askey and Tom H. Koornwinder and Walter J.
Schempp",
title = "Special Functions: Group Theoretical Aspects and
Applications",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxiv + 311",
year = "2001",
ISBN = "90-277-1822-9",
ISBN-13 = "978-90-277-1822-8",
LCCN = "QA1 M428 v. 18 c.2",
bibdate = "Sat Oct 30 17:58:21 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics and Its Applications",
acknowledgement = ack-nhfb,
}
@Article{Bashagha:2001:NRS,
author = "A. E. Bashagha",
title = "Novel radix-$2$ $k$ square root module",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "148",
number = "4",
pages = "190--196",
month = aug,
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The conventional two's complement radix-$2$ $k$ square
root algorithm requires a set of $2^k$ full precision
comparisons to generate all the $2^k$ possible values
of the partial remainder. The correct remainder is the
minimum \ldots{}",
}
@Article{Berry:2001:WSF,
author = "Michael Berry",
title = "Why are special functions special?",
journal = j-PHYS-TODAY,
volume = "54",
number = "4",
pages = "11--12",
year = "2001",
CODEN = "PHTOAD",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
bibdate = "Sat Feb 19 13:23:33 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Boisvert:2001:MM,
author = "Ronald F. Boisvert and M. J. Donahue and Daniel W.
Lozier and R. McMichael and B. W. Rust",
title = "Mathematics and Measurement",
journal = "NIST Journal of Research",
volume = "106",
number = "1",
pages = "293--313",
month = jan # "\slash " # feb,
year = "2001",
bibdate = "Fri Jul 09 06:26:11 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgess:2001:DIR,
author = "N. Burgess and C. Hinds",
booktitle = "Conference Record of the Thirty-Fifth Asilomar
Conference on Signals, Systems and Computers, 2001",
title = "Design issues in radix-$4$ {SRT} square root {\&}
divide unit",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1646--1650",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper introduces a number of design issues not
covered in the open literature that arose during the
design of a radix-$4$ SRT divide/square root unit for a
vector processing chip. These include compression of
the partial remainder's m.s.b.'s, \ldots{}",
}
@Book{Bustoz:2001:SFC,
editor = "Joaquin Bustoz and Mourad Ismail and S. K. (Sergei
Konstantinovich) Suslov",
title = "Special functions 2000: current perspective and future
directions",
volume = "30",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xi + 520",
year = "2001",
ISBN = "0-7923-7119-4, 0-7923-7120-8",
ISBN-13 = "978-0-7923-7119-9, 978-0-7923-7120-5",
LCCN = "QA351 .S694 2001",
bibdate = "Sat Oct 30 17:31:39 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "NATO science series. Series II, Mathematics, physics,
and chemistry",
acknowledgement = ack-nhfb,
subject = "functions, special; congresses",
tableofcontents = "Preface \\
Foreword \\
Bailey's transform, lemma, chains and tree / George E.
Andrews 1 \\
Riemann--Hilbert problems for multiple orthogonal
polynomials / Walter Van Assche, Jeffrey S. Geronimo,
Arno B. J. Kuijlaars 23 \\
Flowers which we cannot yet see growing in Ramanujan's
garden of hypergeometric series, elliptic functions and
$q$'s / Bruce C. Berndt 61 \\
Orthogonal rational functions and continued fractions
[et al.] 87 \\
Orthogonal polynomials and reflection groups / Charles
F. Dunkl 111 \\
The bispectral problem: an overview / F. Alberto
Grunbaum 129 \\
The Bochner--Krall problem: some new perspectives / Luc
Haine 141 \\
Lectures on $q$-orthogonal polynomials / Mourad E. H.
Ismail 179 \\
The Askey--Wilson function transform scheme / Erik
Koelink, Jasper V. Stokman 221 \\
Arithmetic of the partition function / Ken Ono 243 \\
The associated classical orthogonal polynomials / Mizan
Rahman 255 \\
Special functions defined by analytic difference
equations / S. N. M. Ruijsenaars 281 \\
The factorization method, self-similar potentials and
quantum algebras / V. P. Spiridonov 335 \\
Generalized eigenvalue problem and a new family of
rational functions biorthogonal on elliptic grids / V.
P. Spiridonov, A. S. Zhedanov 365 \\
Orthogonal polynomials and combinatorics / Dennis
Stanton 389 \\
Basic exponential functions on a $q$-quadratic grid /
Sergei K. Suslov 411 \\
Projection operator method for quantum groups / V. N.
Tolstoy 457 \\
Uniform asymptotic expansions / R. Wong 489 \\
Exponential asymptotics / R. Wong 505 \\
Index 519",
}
@InCollection{Corless:2001:RAE,
author = "Robert M. Corless and James H. Davenport and David J.
Jeffrey and Gurjeet Litt and Stephen M. Watt",
booktitle = "Artificial intelligence and symbolic computation
(Madrid, 2000)",
title = "Reasoning about the elementary functions of complex
analysis",
volume = "1930",
publisher = pub-SV,
address = pub-SV:adr,
pages = "115--126",
year = "2001",
MRclass = "68W30 (30C35)",
MRnumber = "MR1882755 (2002m:68126)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Comput. Sci.",
acknowledgement = ack-nhfb,
}
@Article{Eklund:2001:CEF,
author = "Neil Eklund",
title = "{CORDIC}: elementary function computation using
recursive sequences",
journal = j-COLLEGE-MATH-J,
volume = "32",
number = "5",
pages = "330--333",
year = "2001",
ISSN = "0746-8342",
MRclass = "65D20",
MRnumber = "MR1868594",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "The College Mathematics Journal",
}
@Book{Garvan:2001:SCN,
editor = "Frank (Frank G.) Garvan and Mourad Ismail",
title = "Symbolic computation, number theory, special
functions, physics, and combinatorics",
volume = "4",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "x + 283",
year = "2001",
ISBN = "1-4020-0101-0",
ISBN-13 = "978-1-4020-0101-7",
LCCN = "QA295 .S86 2001",
bibdate = "Sat Oct 30 17:31:50 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Developments in mathematics",
acknowledgement = ack-nhfb,
subject = "q-series; Congresses; Algebra; Data processing; Number
theory; Functions, Special; Mathematical physics;
Combinatorial analysis",
}
@Unpublished{Godfrey:2001:NCC,
author = "P. Godfrey",
title = "A Note on the Computation of the Convergent {Lanczos}
Complex Gamma Approximation",
year = "2001",
bibdate = "Mon Nov 24 21:04:40 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Unpublished Web file.",
URL = "http://my.fit.edu/~gabdo/gamma.txt",
acknowledgement = ack-nhfb,
}
@InProceedings{Lang:2001:CRR,
author = "Tom{\'a}s Lang and Elisardo Antelo",
booktitle = "Proceedings of the 15th IEEE Symposium on Computer
Arithmetic, 11--13 June 2001",
title = "Correctly Rounded Reciprocal Square-Root by Digit
Recurrence and Radix-$4$ Implementation",
crossref = "Burgess:2001:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "83--93",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "We present a reciprocal square-root algorithm by digit
recurrence and selection by a staircase function, and
the radix-$4$ implementation. As similar algorithms for
division and square-root, the results are obtained
correctly rounded in a \ldots{}",
}
@TechReport{Li:2001:LLF,
author = "Ren-Cang Li and Peter Markstein and Jon P. Okada and
James W. Thomas",
title = "The {\tt libm} library and floating-point arithmetic
for {HP-UX} on {Itanium}",
type = "Technical report",
institution = "Hewlett--Packard Company",
address = "Palo Alto, CA, USA",
pages = "??",
month = apr,
year = "2001",
bibdate = "Fri Jun 24 20:12:09 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
acknowledgement = ack-nhfb,
}
@Article{Loenko:2001:CEF,
author = "M. Yu. Loenko",
title = "Computation of elementary functions with guaranteed
accuracy",
journal = j-PROGRAMMIROVANIE,
volume = "2",
pages = "68--80",
year = "2001",
CODEN = "PROGD3",
ISSN = "0132-3474, 0361-7688",
MRclass = "65D15 (65G20)",
MRnumber = "MR1867584",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}
@Article{Meyer:2001:JEF,
author = "Kenneth R. Meyer",
title = "{Jacobi} Elliptic Functions from a Dynamical Systems
Point of View",
journal = j-AMER-MATH-MONTHLY,
volume = "108",
number = "8",
pages = "729--737",
month = oct,
year = "2001",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 12:00:14 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i346008;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2695616",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@Article{Muller:2001:CCH,
author = "Keith E. Muller",
title = "Computing the confluent hypergeometric function,
{$M(a,b,x)$}",
journal = j-NUM-MATH,
volume = "90",
number = "1",
pages = "179--196",
month = nov,
year = "2001",
CODEN = "NUMMA7",
DOI = "http://dx.doi.org/10.1007/s002110100285",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
bibdate = "Sun Feb 3 10:07:57 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/nummath2000.bib",
URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm;
http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
}
@Article{Nagel:2001:EHF,
author = "Bengt Nagel",
title = "An expansion of the hypergeometric function in
{Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "42",
number = "12",
pages = "5910--5914",
month = dec,
year = "2001",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Thu Mar 28 19:47:21 MST 2002",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
}
@Article{Rabi:2001:OCA,
author = "J. A. Rabi and M. J. S. de Lemos",
title = "Optimization of convergence acceleration in multigrid
numerical solutions of conductive-convective problems",
journal = j-APPL-MATH-COMP,
volume = "124",
number = "2",
pages = "215--226",
day = "25",
month = oct,
year = "2001",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
bibdate = "Sun Nov 18 09:58:00 MST 2001",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Rahavachary:2001:LSS,
author = "Saty Rahavachary",
title = "Letters: Setting the {\tt sqrt()} record straight",
journal = j-DDJ,
volume = "26",
number = "4",
pages = "12--12",
month = apr,
year = "2001",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Mar 13 15:22:36 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ddj.com/",
acknowledgement = ack-nhfb,
}
@Article{Rump:2001:RPS,
author = "Siegfried M. Rump",
title = "Rigorous and Portable Standard Functions",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "3",
pages = "540--562",
month = jun,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1023/A:1021971313412",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
http://www.mai.liu.se/BIT/contents/bit41.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
abstract = "Today's floating point implementations of elementary
transcendental functions are usually very accurate.
However, with few exceptions, the actual accuracy is
not known. In the present paper we describe a rigorous,
accurate, fast and portable implementation of the
elementary standard functions based on some existing
approximate standard functions. The scheme is outlined
for IEEE 754, but not difficult to adapt to other
floating point formats. A Matlab implementation is
available on the net. Accuracy of the proposed
algorithms can be rigorously estimated. As an example
we prove that the relative accuracy of the exponential
function is better than 2.07 eps in a slightly reduced
argument range (eps denoting the relative rounding
error unit). Otherwise, extensive computational tests
suggest for all elementary functions and all suitable
arguments an accuracy better than about 3 eps.",
acknowledgement = ack-nhfb,
keywords = "elementary functions; floating-point arithmetic",
}
@Article{Smith:2001:AFS,
author = "David M. Smith",
title = "{Algorithm 814}: {Fortran 90} software for
floating-point multiple precision arithmetic, gamma and
related functions",
journal = j-TOMS,
volume = "27",
number = "4",
pages = "377--387",
month = dec,
year = "2001",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Wed Mar 13 08:49:29 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Takagi:2001:HAC,
author = "N. Takagi",
booktitle = "Proceedings of the 15th IEEE Symposium on Computer
Arithmetic, 11--13 June 2001",
title = "A Hardware Algorithm for Computing Reciprocal Square
Root",
crossref = "Burgess:2001:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "94--100",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC
Proceedings database",
acknowledgement = ack-nhfb,
summary = "A hardware algorithm for computing the reciprocal
square root which appears frequently in multimedia and
graphics applications is proposed. The reciprocal
square root is computed by iteration of
carry-propagation-free additions, shifts, and
\ldots{}",
}
@Article{Thorsley:2001:AEH,
author = "Michael D. Thorsley and Marita C. Chidichimo",
title = "An asymptotic expansion for the hypergeometric
function {$_2F_1( a, b; c; x )$}",
journal = j-J-MATH-PHYS,
volume = "42",
number = "4",
pages = "1921--1930",
month = apr,
year = "2001",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Apr 18 05:33:53 MDT 2001",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
}
@Article{Verdonk:2001:PRIa,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A precision- and range-independent tool for testing
floating-point arithmetic {I}: {Basic} operations,
square root, and remainder",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "92--118",
month = mar,
year = "2001",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/382043.382404",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://doi.acm.org/10.1145/382043.382404;
http://www.win.ua.ac.be/~cant/ieeecc754.html",
abstract = "This paper introduces a precision- and
range-independent tool for testing the compliance of
hardware or software implementations of
(multiprecision) floating-point arithmetic with the
principles of the IEEE standards 754 and 854. The tool
consists of a driver program, offering many options to
test only specific aspects of the IEEE standards, and a
large set of test vectors, encoded in a
precision-independent syntax to allow the testing of
basic and extended hardware formats as well as
multiprecision floating-point implementations. The
suite of test vectors stems on one hand from the
integration and fully precision- and range-independent
generalization of existing hardware test sets, and on
the other hand from the systematic testing of exact
rounding for all combinations of round and sticky bits
that can occur. The former constitutes only 50\% of the
resulting test set. In the latter we especially focus
on hard-to-round cases. In addition, the test suite
implicitly tests properties of floating-point
operations, following the idea of Paranoia, and it
reports which of the three IEEE-compliant underflow
mechanisms is used by the floating-point implementation
under consideration. We also check whether that
underflow mechanism is used consistently. The tool is
backward compatible with the UCBTEST package and with
Coonen's test syntax.",
accepted = "23 February 2001",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
keywords = "arithmetic; floating-point; floating-point testing;
IEEE floating-point standard; multiprecision;
validation; Verification",
subject = "Primary Classification: G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
arithmetic\\
Additional Classification: D. Software D.3 PROGRAMMING
LANGUAGES D.3.0 General Subjects: Standards",
}
@Article{Weniger:2001:IID,
author = "Ernst Joachim Weniger",
title = "Irregular input data in convergence acceleration and
summation processes: {General} considerations and some
special {Gaussian} hypergeometric series as model
problems",
journal = j-COMP-PHYS-COMM,
volume = "133",
number = "2--3",
pages = "202--228",
day = "15",
month = jan,
year = "2001",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(00)00175-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 01 09:12:48 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
keywords = "convergence acceleration",
remark = "This paper concentrates on $_2F_1(a,b;c;z)$.",
}
@InProceedings{Zheng:2001:ARE,
author = "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
booktitle = "Proceedings of the 4th International Conference on
ASIC",
title = "The application of redundant encoding in iterative
implementation of division and square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "603--606",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this paper is to discuss the speed
improvement in division and square root computation
with small area penalty. The digit recurrence SRT
algorithm and functional iteration Newton--Raphson
algorithm are generally used in modern \ldots{}",
}
@Misc{Ziv:2001:APM,
author = "Abraham Ziv and Moshe Olshansky and Ealan Henis and
Anna Reitman",
title = "Accurate Portable Mathematical Library ({IBM
APMathLib})",
howpublished = "World-Wide Web document",
publisher = pub-IBM,
address = pub-IBM:adr,
day = "20",
month = dec,
year = "2001",
bibdate = "Wed Nov 24 08:06:54 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
http://oss.software.ibm.com/mathlib/",
acknowledgement = ack-nhfb,
}
@InCollection{Boisvert:2002:HMF,
author = "Ronald F. Boisvert and Daniel W. Lozier",
title = "Handbook of Mathematical Functions",
crossref = "Lide:2002:CEM",
pages = "135--139",
year = "2002",
bibdate = "Fri Jul 09 06:28:13 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Also printed as NIST Special Publication 958, Jan.
2001.",
acknowledgement = ack-nhfb,
}
@Article{Bradford:2002:RAE,
author = "Russell Bradford and Robert M. Corless and James H.
Davenport and David J. Jeffrey and Stephen M. Watt",
title = "Reasoning about the elementary functions of complex
analysis",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "36",
number = "3",
pages = "303--318",
year = "2002",
CODEN = "AMAIEC",
ISSN = "1012-2443",
MRclass = "30-01 (03B35 68W30)",
MRnumber = "MR1950025 (2003m:30001)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Artificial intelligence and symbolic computation
(Madrid, 2000)",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics and Artificial Intelligence",
}
@InProceedings{Bradford:2002:TBS,
author = "Russell Bradford and James H. Davenport",
booktitle = "Proceedings of the 2002 International Symposium on
Symbolic and Algebraic Computation",
title = "Towards better simplification of elementary
functions",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "16--22 (electronic)",
year = "2002",
MRclass = "68W30 (33B10)",
MRnumber = "MR2035228",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:2002:GQA,
author = "W. Gautschi",
title = "{Gauss} quadrature approximations to hypergeometric
and confluent hypergeometric functions",
journal = j-J-COMP-APPL-MATH,
volume = "139",
number = "1",
pages = "173--187",
day = "1",
month = feb,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33F05 (33C05 33C15 65D20)",
MRnumber = "MR1876879 (2002m:33029)",
bibdate = "Thu Dec 01 09:11:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
remark = "The paper treats ordinary and confluent hypergeometric
functions $_2F_1$ and $_1F_1$, using their integral
representations to obtain Gaussian quadrature rules.",
}
@Article{Gil:2002:AAB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
routines for the computation of complex {Airy}
functions",
journal = j-TOMS,
volume = "28",
number = "3",
pages = "325--336",
month = sep,
year = "2002",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/569147.569150",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Nov 9 11:16:50 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Two Fortran 77 routines for the evaluation of Airy
functions of complex arguments $Ai(z)$, $Bi(z)$ and
their derivatives are presented. The routines are based
on the use of Gaussian quadrature, Maclaurin series and
asymptotic expansions. Comparison with a previous code
by D. E. Amos (ACM TOMS 12 (1986)) is provided.",
acknowledgement = ack-nhfb,
}
@Article{Gil:2002:AGH,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
routines for the computation of complex {Scorer}
functions",
journal = j-TOMS,
volume = "28",
number = "4",
pages = "436--447",
month = dec,
year = "2002",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/592843.592847",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Mar 28 08:17:55 MST 2003",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Two Fortran 77 routines for the evaluation of Scorer
functions of complex arguments $Gi(z)$, $Hi(z)$ and
their derivatives are presented. The routines are based
on the use of quadrature, Maclaurin series and
asymptotic expansions. For real $z$ comparison with a
previous code by A. J. Macleod (J. Comput. Appl. Math.
53 (1994)) is provided.",
acknowledgement = ack-nhfb,
}
@TechReport{Gil:2002:CSF,
author = "A. Gil and J. Segura and N. M. Temme",
title = "Computing special functions by using quadrature
rules",
type = "Report",
number = "MAS-R0230",
institution = "Centrum voor Wiskunde en Informatica",
address = "Amsterdam, The Netherlands",
pages = "11",
year = "2002",
LCCN = "QA9.A1 R426 MAS-R0230",
bibdate = "Sat Oct 30 19:13:12 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Gil:2003:CSF}.",
acknowledgement = ack-nhfb,
}
@Article{Gil:2002:EMB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Evaluation of the Modified {Bessel} Function of the
Third Kind of Imaginary Orders",
journal = j-J-COMPUT-PHYS,
volume = "175",
number = "2",
pages = "398--411",
day = "20",
month = jan,
year = "2002",
CODEN = "JCTPAH",
DOI = "http://dx.doi.org/10.1006/jcph.2001.6894",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:13 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib;
http://www.sciencedirect.com/science/journal/00219991",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999101968949",
abstract = "The evaluation of the modified Bessel function of the
third kind of purely imaginary order
$\mathrm{K}_{ia}(x)$ is discussed; we also present
analogous results for the derivative. The methods are
based on the use of Maclaurin series, nonoscillatory
integral representations, asymptotic expansions, and a
continued fraction method, depending on the ranges of x
and a. We discuss the range of applicability of the
different approaches considered and conclude that power
series, the continued fraction method, and the
nonoscillatory integral representation can be used to
accurately compute the function $\mathrm{K}_{ia}(x)$ in
the range $0 \leq a \leq 200$, $0 \leq x \leq 100$;
using a similar scheme the derivative
$\mathrm{K}'_{ia(x)}$ can also be computed within these
ranges.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
}
@Article{Gray:2002:ARE,
author = "Norman Gray",
title = "Automatic reduction of elliptic integrals using
{Carlson}'s relations",
journal = j-MATH-COMPUT,
volume = "71",
number = "237",
pages = "311--318",
month = jan,
year = "2002",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu Jan 31 06:16:28 MST 2002",
bibsource = "http://www.ams.org/mcom/2002-71-237;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex",
acknowledgement = ack-nhfb,
}
@Book{Korenev:2002:BFT,
author = "B. G. (Boris Grigorevich) Korenev",
title = "{Bessel} functions and their applications",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "ix + 276",
year = "2002",
ISBN = "0-415-28130-X (hardcover)",
ISBN-13 = "978-0-415-28130-0 (hardcover)",
LCCN = "QA408 .K67 2002",
bibdate = "Sat Oct 30 17:01:51 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "Bessel functions",
xxaddress = pub-CRC:adr,
xxpublisher = pub-CRC,
}
@Article{McCluskey:2002:MLF,
author = "Glen McCluskey",
title = "Math Library Functions in {C9X}",
journal = j-LOGIN,
volume = "27",
number = "2",
pages = "8--13",
month = apr,
year = "2002",
CODEN = "LOGNEM",
ISSN = "1044-6397",
bibdate = "Tue Apr 11 10:52:14 MDT 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.usenix.org/publications/login/2002-04/index.html",
URL = "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
acknowledgement = ack-nhfb,
remark = "This is a short tutorial on some of the new math
library functions in C99.",
}
@InProceedings{Pineiro:2002:HRL,
author = "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
booktitle = "{The IEEE International Conference on
Application-Specific Systems, Architectures and
Processors, 2002. Proceedings. 17--19 July 2002}",
title = "High-radix logarithm with selection by rounding",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "101--110",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A high-radix digit-recurrence algorithm or the
computation of the logarithm is presented in this
paper. Selection by rounding is used in iterations
j/spl ges/2, and selection by table in the first
iteration is combined with a restricted digit-set
\ldots{}",
}
@Article{Pineiro:2002:HSD,
author = "J. A. Pi{\~n}eiro and J. D. Bruguera",
title = "High-Speed Double Precision Computation of Reciprocal,
Division, Square Root, and Inverse Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "12",
pages = "1377--1388",
month = dec,
year = "2002",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2002.1146704",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A new method for the high-speed computation of
double-precision floating-point reciprocal, division,
square root, and inverse square root operations is
presented in this paper. This method employs a
second-degree minimax polynomial approximation to
\ldots{}",
}
@Book{Samko:2002:HIT,
author = "S. G. (Stefan Grigorevich) Samko",
title = "Hypersingular integrals and their applications",
volume = "5",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "xvii + 359",
year = "2002",
ISBN = "0-415-27268-8",
ISBN-13 = "978-0-415-27268-1",
LCCN = "QA403.5 .S26 2002",
bibdate = "Sat Oct 30 17:22:10 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "singular integrals",
}
@InProceedings{Sawada:2002:FVD,
author = "J. Sawada",
title = "Formal verification of divide and square root
algorithms using series calculation",
crossref = "Borrione:2002:TIW",
pages = "31--49",
year = "2002",
bibdate = "Fri Jun 24 15:14:00 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sawada:2002:MVS,
author = "Jun Sawada and Ruben Gamboa",
title = "Mechanical Verification of a Square Root Algorithm
Using {Taylor}'s Theorem",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2517",
pages = "274--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743",
bibdate = "Sat Nov 30 20:58:00 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Sebah:2002:IGF,
author = "Pascal Sebah and Xavier Gourdon",
title = "Introduction to the Gamma Function",
howpublished = "World-Wide Web document",
day = "4",
month = feb,
year = "2002",
bibdate = "Sat May 01 16:07:51 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://numbers.computation.free.fr/Constants/constants.html;
http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps",
acknowledgement = ack-nhfb,
}
@Article{Tornaria:2002:SRM,
author = "Gonzalo Tornar{\'\i}a",
title = "Square Roots Modulo $p$",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2286",
pages = "430--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
bibdate = "Tue Sep 10 19:09:12 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
acknowledgement = ack-nhfb,
}
@Book{Vladimirov:2002:MTG,
author = "V. S. (Vasilii Sergeevich) Vladimirov",
title = "Methods of the theory of generalized functions",
volume = "6",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "xiv + 311",
year = "2002",
ISBN = "0-415-27356-0",
ISBN-13 = "978-0-415-27356-5",
LCCN = "QC20.7.T45 V53 2002",
bibdate = "Sat Oct 30 17:22:15 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "Theory of distributions (Functional analysis);
Integral transforms; Mathematical physics",
}
@Article{Abad:2003:AEQ,
author = "J. Abad and J. Sesma",
title = "Asymptotic expansion of the quasiconfluent
hypergeometric function",
journal = j-J-MATH-PHYS,
volume = "44",
number = "4",
pages = "1723--1729",
month = apr,
year = "2003",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:01 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
}
@Article{Agou:2003:SPR,
author = "Simon Joseph Agou and Marc Del{\'e}glise and
Jean-Louis Nicolas",
title = "Short Polynomial Representations for Square Roots
Modulo $p$",
journal = j-DESIGNS-CODES-CRYPTOGR,
volume = "28",
number = "1",
pages = "33--44",
month = jan,
year = "2003",
CODEN = "DCCREC",
ISSN = "0925-1022 (print), 1573-7586 (electronic)",
ISSN-L = "0925-1022",
bibdate = "Thu Dec 11 06:27:20 MST 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.wkap.nl/jrnltoc.htm/0925-1022",
URL = "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Beaumont:2003:BSE,
author = "James Beaumont and Russell Bradford and James H.
Davenport",
booktitle = "Proceedings of the 2003 International Symposium on
Symbolic and Algebraic Computation",
title = "Better simplification of elementary functions through
power series",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "30--36 (electronic)",
year = "2003",
MRclass = "33F10 (68W30)",
MRnumber = "MR2035192 (2005e:33018)",
MRreviewer = "Ekatherina A. Karatsuba",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "A new algorithm testing the correctness of
simplifications of elementary functions in the presence
of branch cuts is proposed.",
}
@Article{Buhring:2003:PSH,
author = "Wolfgang B{\"u}hring",
title = "Partial sums of hypergeometric functions of unit
argument",
journal = j-PROC-AM-MATH-SOC,
volume = "132",
number = "2",
pages = "407--415",
month = "????",
year = "2003",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "33C20",
MRnumber = "MR2022363 (2005f:33011)",
bibdate = "Thu Dec 01 09:53:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}
@TechReport{Cornea:2003:DSR,
author = "M. Cornea and J. Harrison and C. Iordache and B. Norin
and S. Story",
title = "Division, Square Root and Remainder Algorithms for the
{Intel Itanium} Architecture",
type = "Report",
institution = pub-INTEL,
address = pub-INTEL:adr,
month = nov,
year = "2003",
bibdate = "Fri Jun 24 12:05:58 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dominici:2003:NDS,
author = "Diego Dominici",
title = "Nested derivatives: a simple method for computing
series expansions of inverse functions",
journal = j-INT-J-MATH-MATH-SCI,
volume = "58",
pages = "3699--3715",
year = "2003",
CODEN = "????",
ISSN = "0161-1712",
MRclass = "41A58 (33F10)",
MRnumber = "MR2031140 (2005f:41079)",
MRreviewer = "Tord H. Ganelius",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
abstract = "We give an algorithm to compute the series expansion
for the inverse of a given function. The algorithm is
extremely easy to implement and gives the first $N$
terms of the series. We show several examples of its
application in calculating the inverses of some special
functions.",
acknowledgement = ack-nhfb,
keywords = "error function, erf(x); incomplete beta function,
B(nu,mu,x); incomplete gamma function, gamma(nu,x);
logarithm integral, li(x); Maple; sine integral,
Si(x)",
}
@InProceedings{Ercegovac:2003:DRA,
author = "M. D. Ercegovac and J.-M. Muller",
booktitle = "Conference Record of the Thirty-Seventh Asilomar
Conference on Signals, Systems and Computers, 2003",
title = "Digit-recurrence algorithms for division and square
root with limited precision primitives",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1440--1444",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We propose a digit-recurrence algorithm for square
root using limited-precision multipliers, adders, and
table-lookups. The algorithm, except in the
initialization, uses the digit-recurrence algorithm for
division with limited-precision primitives \ldots{}",
}
@Article{Fabijonas:2003:ACM,
author = "B. R. Fabijonas and Daniel W. Lozier and J. M.
Rappoport",
title = "Algorithms and Codes for the {Macdonald} Function:
Recent Progress and Comparisons",
journal = j-J-COMP-APPL-MATH,
volume = "161",
number = "1",
pages = "179--192",
month = "????",
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
MRclass = "33F05 (33C10 65D20)",
MRnumber = "MR2018582",
bibdate = "Fri Jul 09 06:21:51 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
acknowledgement = ack-nhfb,
}
@Article{Galue:2003:FRG,
author = "L. Galu{\'e} and A. Al-Zamel and S. L. Kalla",
title = "Further results on generalized hypergeometric
functions",
journal = j-APPL-MATH-COMP,
volume = "136",
number = "1",
pages = "17--25",
day = "25",
month = mar,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:40:52 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
}
@Article{Gil:2003:CSF,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computing Special Functions by Using Quadrature
Rules",
journal = j-NUMER-ALGORITHMS,
volume = "33",
number = "1--4",
pages = "265--275",
month = aug,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Mon Sep 29 08:37:11 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Intel:2003:DSR,
author = "{Intel}",
title = "Divide, Square Root, and Remainder Algorithms for the
{Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
acknowledgement = ack-nhfb,
}
@Misc{Intel:2003:NID,
author = "{Intel}",
title = "Non-{IEEE} Division, Square Root, Reciprocal, and
Reciprocal Square Root Algorithms for the {Intel
Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
acknowledgement = ack-nhfb,
}
@Article{Kzaz:2003:CAG,
author = "M. Kzaz and M. Pr{\'e}vost",
title = "Convergence Acceleration of {Gauss--Chebyshev}
Quadrature Formulae",
journal = j-NUMER-ALGORITHMS,
volume = "34",
number = "2--4",
pages = "379--391",
month = dec,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Tue Jan 13 17:32:50 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Lang:2003:RRS,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "Radix-$4$ Reciprocal Square-root and Its Combination
with Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "9",
pages = "1100--1114",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2003.1228508",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In this work, we present a reciprocal square root
algorithm by digit recurrence and selection by a
staircase function and the radix-$4$ implementation. As
in similar algorithms for division and square root, the
results are obtained correctly rounded in a
straightforward manner (in contrast to existing methods
to compute the reciprocal square root). Although,
apparently, a single selection function can only be
used for $j \geq 2$ (the selection constants are
different for $j = 0$, $j = 1$, and $j \geq 2$), we
show that it is possible to use a single selection
function for all iterations. We perform a rough
comparison with existing methods and we conclude that
our implementation is a low hardware complexity
solution with moderate latency, especially for exactly
rounded results. We also extend the unit to support
division and square root with the same selection
function and with slight modifications in the
initialization of the reciprocal square root unit.",
acknowledgement = ack-nhfb,
}
@TechReport{Lefevre:2003:WCC,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "Worst Cases for Correct Rounding for the Elementary
Functions in Double Precision",
type = "Technical report",
institution = "INRIA, Projet Spaces, LORIA, Campus Scientifique",
address = "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
France",
day = "14",
month = aug,
year = "2003",
bibdate = "Thu Jul 08 08:27:53 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
abstract = "We give the results of our search for the worst cases
for correct rounding of the major elementary functions
in double precision floating-point arithmetic. These
results allow the design of reasonably fast routines
that will compute these functions with correct
rounding, at least in some interval, for any of the
four rounding modes specified by the IEEE-754 standard.
They will also allow one to easily test libraries that
are claimed to provide correctly rounded functions.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; elementary functions;
floating-point arithmetic; Table Maker's Dilemma",
}
@Article{Lozier:2003:NDL,
author = "Daniel W. Lozier",
title = "{NIST Digital Library of Mathematical Functions}",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "38",
number = "1--3",
pages = "105--119",
month = may,
year = "2003",
CODEN = "AMAIEC",
ISSN = "1012-2443",
bibdate = "Fri Jul 09 06:23:08 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
acknowledgement = ack-nhfb,
}
@InProceedings{Markstein:2003:FQP,
author = "Peter Markstein",
title = "A fast quad precision elementary function library for
{Itanium}",
crossref = "Anonymous:2003:CRN",
pages = "5--12",
year = "2003",
bibdate = "Fri Jun 24 20:14:39 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This talk will describe Itanium's floating point
architecture and how it has been used to produce a high
performance, highly accurate quad precision elementary
function library.\par
Itanium's floating-point features will first be
described, from the point of view of a computer
architect. Many conflicting requirements vie for
consideration during the design of a new computer
architecture. These include instruction word size,
number of registers, the set of operations, arithmetic
precisions supported, and memory access. Some of the
trade-offs during the design phase will be
discussed.\par
One of the objectives of the original Itanium design
was to accelerate quad precision arithmetic. The talk
will describe how the Itanium elementary function
library was constructed, with attention to performance
and accuracy. Because a pair of double-extended
floating point words are used for internal operations
involving quad precision numbers, intermediate results,
holding 128 bits, provide 15 guard bits during
intermediate calculations, resulting in a very low
percentage of misrounded results.",
acknowledgement = ack-nhfb,
}
@Article{Ovtchinnikov:2003:CEGb,
author = "E. Ovtchinnikov",
title = "Convergence Estimates for the Generalized {Davidson}
Method for Symmetric Eigenvalue Problems {II}: The
Subspace Acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "41",
number = "1",
pages = "272--286",
month = feb,
year = "2003",
CODEN = "SJNAAM",
DOI = "http://dx.doi.org/10.1137/S0036142902411768",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
bibdate = "Fri Aug 15 05:57:09 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41176",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Paszkowski:2003:CAS,
author = "Stefan Paszkowski",
title = "Convergence Acceleration of Some Continued Fractions",
journal = j-NUMER-ALGORITHMS,
volume = "32",
number = "2--4",
pages = "193--247",
month = apr,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Mon Sep 29 08:37:11 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Pineiro:2003:LHR,
author = "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
booktitle = "{ISCAS '03. Proceedings of the 2003 International
Symposium on Circuits and Systems. 25--28 May 2003}",
title = "On-line high-radix exponential with selection by
rounding",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "IV-121--IV-124",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An on-line high-radix algorithm for computing the
exponential function (e/sup x/) with arbitrary
precision n is presented. Selection by rounding and a
redundant digit-set for the digits e/sub j/ are used,
with selection by table in the first \ldots{}",
}
@Book{Sidi:2003:PEM,
author = "Avram Sidi",
title = "Practical Extrapolation Methods: Theory and
Applications",
volume = "10",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xxii + 519",
year = "2003",
ISBN = "0-521-66159-5",
ISBN-13 = "978-0-521-66159-1",
LCCN = "QA281 .S555 2003",
bibdate = "Mon Jul 5 16:49:09 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge monographs on applied and computational
mathematics",
acknowledgement = ack-nhfb,
subject = "extrapolation",
xxURL = "http://www.loc.gov/catdir/samples/cam033/2002024669.html;
http://www.loc.gov/catdir/description/cam022/2002024669.html;
http://www.loc.gov/catdir/toc/cam024/2002024669.html",
}
@InProceedings{Wang:2003:TDF,
author = "Xiaojun Wang and B. E. Nelson",
booktitle = "FCCM 2003: 11th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, 9--11
April 2003",
title = "Tradeoffs of designing floating-point division and
square root on {Virtex FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "195--203",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Low latency, high throughput and small area are three
major design considerations of an FPGA (field
programmable gate array) design. In this paper, we
present a high radix SRT division algorithm and a
binary restoring square root algorithm. We \ldots{}",
}
@Article{Yousif:2003:CBF,
author = "Hashim A. Yousif and Richard Melka",
title = "Computing {Bessel} functions of the second kind in
extreme parameter regimes",
journal = j-COMP-PHYS-COMM,
volume = "151",
number = "1",
pages = "25--34",
day = "1",
month = mar,
year = "2003",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.1016/S0010-4655(02)00697-5",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:41:27 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465502006975",
abstract = "A useful method of computing the integral order Bessel
functions of the second kind $Y_n(x+iy)$ when either,
the absolute value of the real part, or the imaginary
part of the argument $z=x+iy$ is small, is described.
This method is based on computing the Bessel functions
for extreme parameter regimes when $x \sim 0$ (or $y
\sim 0$) and is useful because a number existing
algorithms and methods fail to give correct results for
small $x$ or small $y$. The approximating equations are
derived by expanding the Bessel function in Taylor
series, are tested and discussed. The present work is a
continuation of the previous one conducted in regard to
the Bessel function of the first kind. The results of
our formalism are compared to the available existing
numerical methods used in Mathematica, IMSL, MATLAB,
and the Amos library. Our numerical method is easy to
implement, efficient, and produces reliable results. In
addition, this method reduces the computation of the
Bessel functions of the second complex argument to that
of real argument which simplify the computation
considerably.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@Book{Bell:2004:SFS,
author = "W. W. (William Wallace) Bell",
title = "Special functions for scientists and engineers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xiv + 247",
year = "2004",
ISBN = "0-486-43521-0",
ISBN-13 = "9780486435213",
LCCN = "QA351 .B4 2004",
bibdate = "Sat Oct 30 16:30:44 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Dover books on mathematics",
acknowledgement = ack-nhfb,
remark = "Reprinting of \cite{Bell:1968:SFS}.",
subject = "Functions, Special",
}
@Article{Berrut:2004:APS,
author = "Jean-Paul Berrut and Hans D. Mittelmann",
title = "Adaptive Point Shifts in Rational Approximation with
Optimized Denominator",
journal = j-J-COMP-APPL-MATH,
volume = "164--165",
number = "??",
pages = "81--92",
day = "1",
month = mar,
year = "2004",
CODEN = "JCAMDI",
DOI = "http://dx.doi.org/10.1016/S0377-0427(03)00485-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
bibdate = "Tue Mar 24 21:10:48 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the 10th International Congress on
Computational and Applied Mathematics University of
Leuven, Belgium, 22--26 July 2002. Edited by M.J.
Goovaerts, S. Vandewalle, and L. Wuytack.",
abstract = "Classical rational interpolation is known to suffer
from several drawbacks, such as unattainable points and
randomly located poles for a small number of nodes, as
well as an erratic behavior of the error as this number
grows larger. In a former article, we have suggested to
obtain rational interpolants by a procedure that
attaches optimally placed poles to the interpolating
polynomial, using the barycentric representation of the
interpolants. In order to improve upon the condition of
the derivatives in the solution of differential
equations, we have then experimented with a conformal
point shift suggested by Kosloff and Tal-Ezer. As it
turned out, such shifts can achieve a spectacular
improvement in the quality of the approximation itself
for functions with a large gradient in the center of
the interval. This leads us to the present work which
combines the pole attachment method with shifts
optimally adjusted to the interpolated function. Such
shifts are also constructed for functions with several
shocks away from the extremities of the interval.",
acknowledgement = ack-nhfb,
keywords = "interpolation; optimal interpolation; point shifts;
rational approximation",
}
@Article{Brisebarre:2004:ACR,
author = "N. Brisebarre and J.-M. Muller and Saurabh Kumar
Raina",
title = "Accelerating correctly rounded floating-point division
when the divisor is known in advance",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "8",
pages = "1069--1072",
month = aug,
year = "2004",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2004.37",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We present techniques for accelerating the
floating-point computation of $x/y$ when $y$ is known
before $x$. The proposed algorithms are oriented toward
architectures with available fused-mac operations. The
goal is to get exactly the same result as with
\ldots{}",
acknowledgement = ack-nhfb,
summary = "We present techniques for accelerating the
floating-point computation of x/y when y is known
before x. The proposed algorithms are oriented toward
architectures with available fused-mac operations. The
goal is to get exactly the same result as with
\ldots{}",
}
@Article{Chaudhry:2004:EHC,
author = "M. Aslam Chaudhry and Asghar Qadir and H. M.
Srivastava and R. B. Paris",
title = "Extended hypergeometric and confluent hypergeometric
functions",
journal = j-APPL-MATH-COMP,
volume = "159",
number = "2",
pages = "589--602",
day = "6",
month = dec,
year = "2004",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Jul 4 09:15:38 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
}
@Article{Croot:2004:ACC,
author = "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
title = "The {\em abc\/} conjecture and correctly rounded
reciprocal square roots",
journal = j-THEOR-COMP-SCI,
volume = "315",
number = "2--3",
pages = "405--417",
day = "6",
month = may,
year = "2004",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Thu Nov 4 10:19:15 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/tcs2000.bib;
http://www.sciencedirect.com/science/journal/03043975",
abstract = "The reciprocal square root calculation $\alpha =
1/\sqrt{x}$ is very common in scientific computations.
Having a correctly rounded implementation of it is of
great importance in producing numerically predictable
code among today's heterogeneous computing environment.
Existing results suggest that to get the correctly
rounded $\alpha$ in a floating point number system with
$p$ significant bits, we may have to compute up to
$3p+1$ leading bits of $\alpha$. However, numerical
evidence indicates the actual number may be as small as
$2p$ plus a few more bits. This paper attempts to
bridge the gap by showing that this is indeed true,
assuming the {\em abc\/} conjecture which is widely
purported to hold. (But our results do not tell exactly
how many more bits beyond the $2p$ bits, due to the
fact that the constants involved in the conjecture are
ineffective.) Along the way, rough bounds which are
comparable to the existing ones are also proven. The
technique used here is a combination of the classical
Liouville's estimation and contemporary number
theory.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
}
@Article{Defour:2004:PSM,
author = "David Defour and Guillaume Hanrot and Vincent
Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
and Paul Zimmermann",
title = "Proposal for a Standardization of Mathematical
Function Implementation in Floating-Point Arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "367--375",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
acknowledgement = ack-nhfb,
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@InProceedings{Doss:2004:FBI,
author = "C. C. Doss and R. L. {Riley, Jr.}",
booktitle = "FCCM 2004. 12th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "{FPGA}-based implementation of a robust {IEEE-754}
exponential unit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--238",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This work explores the feasibility of implementing a
floating-point exponentiation unit on reconfigurable
computing systems. A table-driven exponentiation unit
was implemented using synthesizable VHDL. The project
included creating pipelined \ldots{}",
}
@TechReport{Ercegovac:2004:CSRa,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
title = "Complex Square Root with Operand Prescaling",
type = "Research Report",
number = "RR2004-42",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 12",
month = sep,
year = "2004",
bibdate = "Mon Dec 06 11:07:40 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
abstract = "We propose a radix-$r$ digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit recurrence
approach allows correct rounding of the result. The
algorithm, compatible with the complex division, and
its design are described at a high-level. We also give
rough comparisons of its latency and cost with respect
to implementation based on standard floating-point
instructions as used in software routines for complex
square root.",
acknowledgement = ack-nhfb,
keywords = "complex square-root; Computer arithmetic;
digit-recurrence algorithm; operand prescaling.",
}
@InProceedings{Ercegovac:2004:CSRb,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
booktitle = "{Proceedings of the 15th IEEE International Conference
on Application-Specific Systems, Architectures and
Processors, 2004}",
title = "Complex square root with operand prescaling",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--62",
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1109/ASAP.2004.1342458",
ISBN = "0-7695-2226-2",
ISBN-13 = "978-0-7695-2226-5",
ISSN = "1063-6862",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We propose a radix-r digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit \ldots{}",
}
@Article{Fabijonas:2004:AAF,
author = "B. R. Fabijonas",
title = "{Algorithm 838}: {Airy} Functions",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "491--501",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/1039813.1039819",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present a Fortran 90 module, which computes the
solutions and their derivatives of Airy's differential
equation, both on the real line and in the complex
plane. The module also computes the zeros and
associated values of the solutions and their
derivatives, and the modulus and phase functions on the
negative real axis. The computational methods are
numerical integration of the differential equation and
summation of asymptotic expansions for large argument.
These methods were chosen because they are simple,
adaptable to any precision, and amenable to rigorous
error analysis. The module can be used to validate
other codes or as a component in programs that require
Airy functions.",
acknowledgement = ack-nhfb,
}
@Article{Fabijonas:2004:CCA,
author = "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
title = "Computation of complex {Airy} functions and their
zeros using asymptotics and the differential equation",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "471--490",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/1039813.1039818",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We describe a method by which one can compute the
solutions of Airy's differential equation, and their
derivatives, both on the real line and in the complex
plane. The computational methods are numerical
integration of the differential equation and summation
of asymptotic expansions for large argument. We give
details involved in obtaining all of the parameter
values, and we control the truncation errors
rigorously. Using the same computational methods, we
describe an algorithm that computes the zeros and
associated values of the Airy functions and their
derivatives, and the modulus and phase functions on the
negative real axis.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gebali:2004:EAF,
author = "Fayez Gebali and Mohamed Watheq El-Kharashi",
title = "{ERL}: an algorithm for fast evaluation of
exponential, reciprocal, and logarithmic functions",
crossref = "Wahdan:2004:IHE",
pages = "269--272",
year = "2004",
bibdate = "Sat Jul 16 18:04:58 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A fast algorithm (ERL) is proposed for evaluating
Exponential, Reciprocal, and Logarithmic functions. The
algorithm requires two to three iterations to complete
using simple operations such as multiply, accumulate,
and table lookup. The algorithm is independent of the
number format used by the machine. Thus it can be
implemented using the IEEE 754 floating-point standard
or any other special format used by special-purpose
processors. The dynamic range of the algorithm is
limited only by the dynamic range of the machine on
which it is implemented Numerical simulations are
performed which verifies the speed and accuracy of the
algorithm.",
acknowledgement = ack-nhfb,
}
@Article{Gil:2004:AMB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 831}: {Modified} {Bessel} functions of
imaginary o